11 10 3494 https://omeka.ibu.edu.ba/files/original/348bd6478e5f90727e526188c6b5f31f.pdf ddb6f3b301a2b0e042f740d13953ddbb PDF Text Text International Conference on Economic and Social Studies, 10-11 May, 2013, Sarajevo A Model for Discrete Time/Space Approximation of the Vasicek Model for the Interest Rate Nedim Gavranovic American University in Bosnia and Herzegovina, Sarajevo, Bosnia and Herzegovina nedimg@bih.net.ba In this paper we present the mathematical model for the real interest rate as an autoregressive discrete time and discrete state space process. The process is an approximation of Vasicek continuous time–space autoregressive process presented in Vasicek (1977). We choose Vasicek model for interest rate for developing bond prices as the one which is used in the analysis of optimal asset allocation problems by many authors. It is a type of one factor short rate model where interest rate movements are driven by one source of market risk. Our model can be used in many applications when modelling an interest rate mathematically or for making simulations on the computer. The shortcoming of Vasicek model is the positive probability of the negative value of interest rate. Due to mean reverting characteristic of the interest rate, even for the negative value of real interest rate, there will be a certain demand for both traditional and index–linked bonds. It is possible to derive the bond market model using the interest rate which does not allow the negative values of the interest rate, for example Cox–Ingersoll–Ross model (Cox et al (1985)). Although CIR model may be more appropriate, and the one and ten years rolling bonds market model can be developed using CIR model, it would be also computationally more demanding. In our model we assume that the discrete time interval is one year. We will show below the technique to transform the continuous time Vasicek process into a discrete time one. We assume that the interest rate can take a finite number of values in a reasonable range. As the Vasicek process transformed into discrete time is still a continuous state space process we use the technique from Tauchen and Hussey (1991) and as a result we get a process with discrete time–state space. Once we obtain a discrete time–state process for real interest rate we can model bond prices as the expected present value of future incomes from the bond. As we assume a zero coupon bond, it means that the bond price is expected present value of one money unit that will be due in n years’ time, where n years is the bond duration. Following the Vasicek approach, we can also introduce a market price of risk. As a final result we get the approximation of the bond market. Keywords: Discrete Time, the Vasicek Model, Interest Rate. 222 � https://omeka.ibu.edu.ba/files/original/ac1d525ba601f25b7da7e9c991299026.docx 84986936495e6e1caf7741cde1d67da6 https://omeka.ibu.edu.ba/files/original/88022d4a4a547b75777c1cf81c4d6972.pdf 11f0ea660fd6ee84c012f7a1e884e523 PDF Text Text International Conference on Economic and Social Studies (ICESoS’13), 10-11 May, 2013, Sarajevo A Bond Market Model Based onDiscrete Time/State Space Approximation of the Vasicek Model Nedim Gavranović American University in Bosnia and Herzegovina, Sarajevo, Bosnia and Herzegovina nedimg@bih.net.ba Abstract In this paper we present the mathematical model for the interest rate (either real or nominal) as an autoregressive discrete time and discrete state space process. Having defined an interest rate model with discrete time/state spaces, we derive zerocoupon prices for bonds with any duration and any initial value of the interest rate. The process is an approximation of Vasicek continuous time/state space autoregressive process presented in Vasicek (1977). We choose Vasicek model for interest rate for developing bond prices as the one which is used in the analysis of optimal asset allocation problems by many authors. It is a type of one factor short rate model where interest rate movements are driven by one source of market risk. Our model can be used in many applications when modeling an interest rate or bond prices mathematically. It is particularly suitable for making simulations on the computer. The shortcoming of Vasicek model is the positive probability of the negative value of interest rate. Due to mean reverting characteristic of the interest rate, even for the negative value of interest rate, there will be a certain demand for both traditional and index–linked bonds. It is possible to derive the bond market model using the interest rate which does not allow the negative values of the interest rate, for example Cox–Ingersoll–Ross model (Cox et al (1985)). Although CIR model may be deemed as a more appropriate, it would be also computationally more demanding. In our model we assume that the discrete time interval is one year. We will show the technique to transform the continuous time Vasicek process into a discrete time one. As the Vasicek process is transformed into discrete time process, it is still a continuous state space process. We use the technique from Tauchen and Hussey (1991) and as a result get a process with discrete time/state spaces. Once we obtain a discrete time/state process for interest rate we can model bond prices as the expected present value of future incomes from the bond. We model a zero coupon bond. Thus, the bond price is expected present value of one money unit that will be due in n years, where n years is the bond duration. Following the Vasicek approach, we can also introduce a market price of risk. As a final result we get the model for the zero-coupon bond prices for the whole bond market (different durations) and for different states of economy (different known values of the interest rate). Keywords: interest rate; Vasicek model, AR(1) process; approximation; computer modeling; discrete time/state spaces, bond market model Introduction In different financial models, one needs to decide if the assumption of constant inflation or constant interest rate is an acceptable approximation. Namely, under this assumption the model does not recognize the risk of inflation or interest rate risk. Adding these risks in the model give us the new insight into the importance of these risks. 1 �International Conference on Economic and Social Studies (ICESoS’13), 10-11 May, 2013, Sarajevo The usual assumption for the interest rate (or inflation) in the model is one of the following: constant, identically independently distributed (iid) random variables for each time period, discrete time stochastic process and continuous time stochastic process. Often, continuous time models better represent the real world. The advantage of a discrete time model over continuous time one is the possibility to solve the problem on computers, and sometimes to obtain the results numerically while the analytical solution is not available with a current mathematical knowledge. In recent years we have witnessed the fast development of computer hardware and software, and of parallel computing. So, when we develop a discrete time model there are very powerful tools for obtaining a numerical solution. Even more, if we want to improve the model, for example to add certain constraints or to add annuities or one or more variables, the improved version of the model still can be solvable. A shortcoming of the numerical solution on the computer is that we usually get one numerical solution for one choice of the values for each parameter. In order to get an idea about the solution for different values of the parameters, we need to get a number of solutions and to compare them numerically. We model the interest rate as an autoregressive discrete time and discrete state space process. The process is an approximation of Vasicek continuous time/state space autoregressive process presented in Vasicek (1977). As the Vasicek model provides bond prices for an implied bond market, we can compare bond prices on the bond market obtained in our model with the one obtained from Vasicek model. Wilkie (1986, 1995) develops a discrete time and state spaces stochastic inflation model similar to our model presented here. Our approach is to start from Vasicek model and develop formulae directly from Vasicek model. For example, our approach can be applied to making discrete time and state spaces approximation of the bond market developed by Boulier et al (2001), and similar reasoning could be applied to the work of Deelstra et al (2000). In our model we assume that the discrete time interval is one year. We assume that interest rate can take finite number of values in a reasonable range. Firstly, the Vasicek process is transformed into discrete time and a continuous state space process. Then, we use the technique from Tauchen and Hussey (1991) and as a result we get a process with discrete time/state space. In Section 2, we present assumptions and the main parts of the Vasicek model. In Section 3, we start from the formulae provided in Vasicek model and derive formulae for discrete model of interest rate. Once we obtain a discrete time/state process for real interest rate we can model bond prices as the expected present value of future income. As we assume a zero coupon bond, it means that the bond price is expected present value of one money unit that will be due in n years, where n years is the bond duration. Following the Vasicek approach, we can also introduce a market price of risk. In Section 4, as a final result we get the approximation of the bond market. The model for the bond market is based on the discrete time/state space interest rate and can be used for computer simulation of the bond market that is consistent with the interest rate. 2 �International Conference on Economic and Social Studies (ICESoS’13), 10-11 May, 2013, Sarajevo The Main Formulae of the Vasicek Model The Vasicek model is used for modeling interest rate where time and state spaces are continuous. It is a continuous time AR (1) process given by drˆt  (a  brˆt )dt   rˆ dWrˆ (t ) (1) where r̂0 is the initial value of the interest rate, a , b and  r̂ are non–negative constants and Wrˆ (t ) is Brownian motion. We use notation rˆt for interest rate from Vasicek model in order to avoid the confusion with interest rate afterwards in this paper. As throughout the whole paper, the sign  above variable denotes it is a random variable. We know that rˆt is a normally distributed random variable and that the conditional expectation and variance of the process given current level r̂0 are a  a E  rˆT     rˆ0   ebT b  b (2)  Var  rˆT   rˆ 1  e2bT  2b (3) 2 for T  0 . The stochastic differential equation of the bond investments is given by dB (T  t , rˆt )   rˆt   B T  t , rˆt  rˆ  dt   B T  t , rˆt  dWrˆ  t  ˆ B(T  t , rt ) (4) where t is the time such that 0  t  T , T is bond duration, B(T , T )  1 , and rˆ   B (T  t , rˆt )  rˆt .  B (T  t , rˆt ) r̂ is referred to as bond's market price of risk and is constant. The function  B (T  t , rˆt ) is given by  B (T  t , rˆt )  1  e  b (T t )  rˆ b for T  t  0 . If we work with zero–coupon bonds and assume that we are interested in the value at time t  0 of the bonds maturing at time T and assuming current value of the interest rate is r̂0 , then the price of the zero–coupon bond is given by 3 (5) �International Conference on Economic and Social Studies (ICESoS’13), 10-11 May, 2013, Sarajevo     1  ebT  B T , rˆ0   Exp   rˆ rˆ   T     b  b 2  1  ebT 2   a 1   rˆ   1  ebT  rˆ2 ˆ Exp  T       r0  3 1  e bT   b 4a   b 2  a    b  (6) Discrete Time/State Space Approximation of the Vasicek Model In order to approximate Vasicek model in discrete time and continuous state space we observe the process Rt  (ad  bd Rt )t   dRR (t ) (7) where R (t )  N (0,1) are independent random variables with normal distribution, for t   . In order to have similar results from the continuous time and discrete time process we fit the parameters ad , bd and  dR into the Vasicek model (1). Let us derive formula for RT using equation (7). We have R1  R0  ad  bd R0   dRR (1) and R  a  (1  b ) R    (1) . 1 Then d d 0 dR R R 2  ad  1  bd  R1   dRR  2   ad  1  bd   ad  1  bd  R0   dRR 1    dRR  2  2 1 2  ad  1  bd   1  bd  R0   dR  1  bd  k 2 k 0 2k k 1 R  k  Continuing the similar reasoning gives us the relation T 1 T k 0 k 1 k T T k RT  ad  1  bd   1  bd  R0   dR  1  bd  R  k  , for T   (8) Knowing that the sum of normally distributed random variables is again normally distributed random variable we have that T  dr  1  bd  k 1 T k  T  k 1 R  k   N  0,  dr2  1  bd  2 T  k    , or  Now, we can easily derive E  RT   ad  a  T   R0  d  1  bd  bd  bd  and 4 (9) �International Conference on Economic and Social Studies (ICESoS’13), 10-11 May, 2013, Sarajevo 1  1  bd  Var  RT    bd  2  bd  2T 2 dR (10) Let us determine the coefficients ad , bd and  dR such that equations (2) and (9), and (3) and (10) respectively, gives the same values. From the first two equations, by equating the expectations, we have that bd  1  eb (11) and ad  a 1  eb b (12) Now, from the second pair of equations, by equating variances, we get  dR   rˆ 1  e2b 2b (13) The discrete time version of the Vasicek process given in (7) is now fully defined and the appropriate parameter values are given in (11)–(13). We have the discrete time and continuous state AR (1) process such that Rt is normally distributed and the conditional expectation and variation of this random variable is the same as the conditional expectation and variance for the Vasicek process given in(1). Thus, we have defined the discrete time and continuous state space approximation of the Vasicek process(1). Tauchen and Hussey (1991) gives the technique for approximating discrete time and continuous state space AR (1) process with a discrete time and state spaces process. We apply this technique to the process(7). In order to deploy the technique from Tauchen and Hussey (1991), we need to choose the density function  ( y) , and the number N denoting the number of Quadrature points. Let the density function  ( y) be the density function of the random variable with the distribution a  N  d ,  dR  .  bd  (14) This choice is based on the proposal in Tauchen and Hussey (1991), where the authors say that this choice works well in most examples. Let us denote with rt random variable which has discrete time and state spaces and which approximate random variable R . It is autoregressive process defined in the form t P rt 1  rt 1;k | rt  rt ; j  5 (15) �International Conference on Economic and Social Studies (ICESoS’13), 10-11 May, 2013, Sarajevo for 1  j, k  N . The constants rt ;i for 1  i  N are the possible states of the interest rate to be defined below. Let the number of Quadrature points be N . The bigger the number of points the better is approximation. However, the choice of N  15 provides quite good behavior and we show the results with the choice of 15 Quadrature points in Appendix. Based on this choice we choose abscissa points, i.e. the possible states of the interest rate are constants rt ;1 , rt ;2 , …, rt ; N , such that the probabilities derived using this technique satisfies the condition P rt 1  rt 1;i | rt  rt ;1   0.02 and P rt 1  rt 1;i | rt  rt ; N   0.02 for 1  i  N and that the points are derived from Gauss Quadrature with these ending points. We derive the weights w1 , …, wN , for these choice of abscissa points and the density function  ( y) . Let us also define the function f  y | r0  as the density function for the random variable with the distribution a   a  N  d   r0  d  1  bd  ,  dr  bd   bd   (16) Having determined the abscissa points, the weighting function and the function f  y | r0  , we can apply the Tauchen and Hussey (1991) technique as follows. Let s  rj    N f  ri | rj  i 1 and let  Njk    rj  f  rk | rj  s  rj    rk  wj wk (17) (18) Then according to Tauchen and Hussey (1991), we have   N ( N ,N ) jk ( j , k ) (1,1)   p jk  ( N ,N ) ( j , k ) (1,1)  P rt 1  rt 1;k | rt  rt ; j  (19) Numerical Derivation of the Bond prices In Section 3, we defined the discrete time/state spaces autoregressive process which approximates the Vasicek model. Now, we derive the zero–coupon bond prices from this process and get the model for the bond market. We first derive the price of the zero–coupon bond with no market price of risk. As usual, it is defined as expected present value of one unit payout after time T . Thus, we have 6 �International Conference on Economic and Social Studies (ICESoS’13), 10-11 May, 2013, Sarajevo B T , r0   E e r1 e r2  ...  e rT  (20) where r1 is a random variable denoting random interest during the first year, r2 is a random variable denoting random interest during the second year knowing r1 , and so on. In order to allow for the existence of the market price of risk, we use the idea from equation (6) and introduce the market price of risk by multiplying the bond price with no market price of risk (equation (20)) with the similar factor as in the continuous time Vasicek model. Let the constant r represents the market price of risk in the Vasicek bond market model. Then we get the equation for the price of a zero–coupon bond as follows B T , r0   e   r r  1     bT T   1 e b b  E e r1 e r2  ...  e rT  (21) Let us explain how we can calculate numerically the bond price in discrete time/state spaces. Following the main formula for the expected value we have that B 1, r0  r0; j   e e   r r  1 e b   r r  1 e b  b  b  b  b  1  E e  r1   1 N  e  r1;k k 1 p jk For the bond of the duration two years we have B  2, r0  r0; j   e   r r  1 e2 b  b  b  2    E e e   e  r1  r2   r r  1 e2 b  b  b  2  N    N  r1;k1  r2;k2  pk1k2  p jk1 e e  k1 1  k2 1  or B  2, r0  r0; j   e   r r  1 e2 b  b  b  2  N   e  r1;k1 k1 1  N  r2;k2  pk1k2  p jk1 e  k2 1  The same pattern is applied for longer durations. However, we can see that the part of the second sum is the same as the sum for the bond with one year duration. Apart from the coefficient for the market price of risk the difference is in the indices only. Using this observation, one can firstly calculate the prices of bonds with the duration of 1 year and for all possible states for r0 and then use these results to obtain the results for the bond with duration of two years. This feature is important when the calculation is applied on the computer. If we define   N B 1, r1  r1;k1   e  r2;k2 k2 1 pk1k2 (22) Then one can write B  2, r0  r0; j   e   r r  1 e2 b  b  b  2  N   e k1 1 Similarly, if we define 7  r1;k1   B 1, r1  r1;k1 p jk1 �International Conference on Economic and Social Studies (ICESoS’13), 10-11 May, 2013, Sarajevo   N B 2, r1  r1;k1   e  r2;k2 k2 1   B 1, r2  r2;k2 pk1k2 then B  3, r0  r0; j   e   r r  1 e3 b  b  b  3  N   e  rk1 k1 1   B 2, r1  r1;k1 p jk1 . Following this pattern, we get an inductive formula for bond prices which significantly reduces computing time. However, we calculate bond prices B T , r0  r0; j  , for 0  T  Tmax and 1  j  N only once and then use the results in the simulations. So, it is important to calculate it in reasonable time only once. Future Research We can use the model and its solution for the investigation of the influence of random inflation or random interest rate in different models. We can also use the results for the models where we need bond prices consistent with a stochastic interest rate. The results are particularly useful for making stochastic simulations on the computer. We model the interest rate using AR(1) Vasicek model. Another model for the interest rate can be used for developing the values of the interest rate in discrete time/statespace environment. The similar technique could be applied to other models as well. Appendix In Appendix, we firstly derive the formula for the exact value of bond prices in discrete time and continuous state space. Then, we compare bond prices derived from the Vasicek model (continuous time/state spaces) with bond prices derive, from the first approximation of the Vasicek model (discrete time and continuous state spaces) and from the second approximation of the Vasicek model (discrete time/state spaces). This Appendix is intended to give the idea of the changes in bond prices due to the approximation. We will not try to evaluate the quality of approximation by any criteria, just to give comparable bond prices values. Equation (20) for the discrete time and continuous state spaces AR(1) process (7) can be solved exactly. Having solved equation (20), we multiply it by the factor  e  r r  1 e T b  b  b  T   (23) for T   and get the exact bond prices in the first approximation of the Vasicek model, where we have discrete time and continuous state spaces. For T  1 equation (20) in discrete time and continuous state spaces can be written as B 1, r0   E e r1   8  e   r1 f  r1 | r0  dr1 (24) �International Conference on Economic and Social Studies (ICESoS’13), 10-11 May, 2013, Sarajevo Knowing that r1 is normally distributed with mean and variance defined in (9) and (10) respectively, we have that B 1, r0    1 e r1 e  2 Var[r1 | r0 ]    r1  E [ r1 |r0 ]2 2Var [ r1 |r0 ] dr1 (25) and B  2, r0   E e r1 e r2 | r0   E e  r2 E e  r1 | r0  | r0   E e r2 B 1, r0  | r0  As we know that r2 is normal random variable, we can derive the solution of the last equation. Having the solution B  2, r0  and multiplying it with factor defined in (23) for T  2 we get the bond price with the duration of two years for any r0   . Continuing this process, we can calculate any B T , r0  , for T  . Multiplying B T , r0  with factor defined in (23) we get bond prices for any duration and any r0   . There is a requirement to have certain relations between bond prices if we want to have a sound model. One way to check the soundness of the bond market model is to compare bond prices derived using the three models for the interest rate. We expect that, for the same duration and for the same initial value of the interest rate, bond prices have similar values. The second important thing we need to have in order to deem the bond prices model as a sound one is to have the same pattern when bond prices are compared in each model. It means that we expect decreasing bond prices as the value of the interest rate during the previous year increases. In Table 1, we present the prices of zero–coupon bonds with the duration of five and ten years and different values of the interest rate during the previous year, for discrete time and state spaces, for discrete time and continuous state space, and for the Vasicek model. 9 �International Conference on Economic and Social Studies (ICESoS’13), 10-11 May, 2013, Sarajevo Table 1: Calculated bond prices for the following values of the parameters: a  0.012 , b  0.6   0.02 and r  0,1528 , and ad  0.009023 , bd  0.451188 and  d  0.015262 . Number of the interest rate states N  15 , the end points for the abscissa are 2.44% and 6.44% . Interest rate Duration 5 year Duration 10 year 1 2 3 –2.44% –2.21% –1.81% Discrete time/state spaces, numerical solution 92.96 92.79 92.49 Discrete time/ continuous state spaces 93.78 93.53 93.10 Continuou s time/state spaces, Vasicek 95.55 95.21 94.60 Discrete time/state spaces, numerical solution 82.35 82.19 81.91 Discrete time/ continuous state spaces 83.20 82.97 82.57 Continuou s time/state spaces, Vasicek 84.84 84.52 83.96 4 –1.25% 92.04 92.50 93.77 81.50 82.01 83.19 5 6 –0.56% 0.22% 91.44 90.73 91.77 90.93 92.75 91.59 80.96 80.30 81.33 80.54 82.24 81.16 7 1.09% 89.92 90.02 90.34 79.56 79.70 79.99 8 9 2.00% 2.91% 89.06 88.21 89.08 88.15 89.05 87.79 78.77 77.99 78.83 77.97 78.80 77.62 10 3.78% 87.42 87.27 86.59 77.27 77.15 76.51 11 12 4.56% 5.25% 86.73 86.17 86.48 85.79 85.50 84.57 76.64 76.12 76.41 75.77 75.50 74.64 13 5.81% 85.74 85.24 83.83 75.73 75.26 73.95 14 6.21% 85.46 84.84 83.30 75.47 74.90 73.46 15 6.44% 85.30 84.62 83.00 75.33 74.69 73.18 We see that long term expected values a / b  0.02 as well as ad / bd  0.02 , as we expected. When we compare bond prices with the same duration in each row we see similar values. For the two presented values of the bond duration, we can see the biggest range of bond prices is for the Vasicek model and the lowest is for discrete time and state spaces. However, observing the columns for the first and for the second approximation of the Vasicek model we can say that bond prices behave quite reasonably in terms of changes as function of the value of the interest rate during the previous year. In Table 2 we present the values of the rates of return on 10 year rolling bonds during one year assuming the value of the interest rate during the previous year being 1.25% and 2.00% . 10 �International Conference on Economic and Social Studies (ICESoS’13), 10-11 May, 2013, Sarajevo Table 2: Rates on 10 year rolling bonds during one year assuming the value of the interest rate during the previous year is 1.25% and 2.00% , and the value of interest the rate in the following year given in the first column. Interest Rate 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 –2.44% –2.21% –1.81% –1.25% –0.56% 0.22% 1.09% 2.00% 2.91% 3.78% 4.56% 5.25% 5.81% 6.21% 6.44% B  9, r1   1 in % B 10, 1.25%  Discrete time/state spaces, numerical solution 3.55 3.36 3.01 2.49 1.81 0.98 0.05 –0.94 –1.92 –2.83 –3.62 –4.27 –4.76 –5.09 –5.27 Discrete time/ continuous state spaces 3.96 3.67 3.17 2.47 1.62 0.65 –0.41 –1.49 –2.57 –3.59 –4.51 –5.31 –5.94 –6.40 –6.66 Continuou s time/state spaces, Vasicek 4.51 4.11 3.42 2.47 1.30 –0.02 –1.45 –2.92 –4.37 –5.74 –6.97 –8.03 –8.88 –9.48 –9.83 B  9, r1   1 in % B 10, 2.00%  Discrete time/state spaces, numerical solution 7.14 6.94 6.57 6.04 5.33 4.48 3.51 2.49 1.48 0.54 –0.28 –0.95 –1.46 –1.80 –1.99 Discrete time continuous state spaces 8.15 7.85 7.33 6.61 5.72 4.71 3.61 2.48 1.36 0.30 –0.66 –1.49 –2.15 –2.62 –2.89 Continuou s time/state spaces, Vasicek 10.33 9.91 9.18 8.18 6.95 5.54 4.03 2.48 0.95 –0.49 –1.79 –2.91 –3.81 –4.44 –4.80 We suppose here that at the beginning of the year we know the value of the interest rate in the previous year and that 10 year zero coupon bond is priced according to that value. This known value of the interest rate is written in the header, and we present examples for the two value r0  1.25% and r0  2.00% . Then we suppose that during the following year the value of the interest rate r1 appears to be as in the first column. At the end of the year we have the price of the 9 year bond and calculate the rate of return on 10 year rolling bonds by B  9, r1  B 10, r0   1 . We can see in Table 2 that the rates of return on 10 year rolling bond investment have the highest range of values for the Vasicek model, the lower for the first approximation and the lowest for the second approximation. It means that in our examples, the variability of bond investment rates is lower compared to the Vasicek model. However, at the same time we can see a regular behavior of returns for both approximations. If  takes lower values than 0.02 , then we get the rates on ten years rolling bond investment using approximations that are more similar to the rates calculated from the Vasicek model. References Boulier J–F, Huang S.J., and Taillard G. (2001).Optimal Management under Stochastic Interest Rates: the Case of a Protected Defined Contribution Pension Fund, Insurance: Mathematics and Economics 28, 173–189. Cox J., Ingersoll J., Ross S. (1985).A Theory of the Term Structure of Interest Rates, Econometrica 53, 385–408. 11 �International Conference on Economic and Social Studies (ICESoS’13), 10-11 May, 2013, Sarajevo Deelstra G., Grasselli M., and Koehl P–F. (2000).Optimal Investment Strategies in a CIR Framework, Journal of Applied Probability 37, 936–946. Duffie D., and Kan R. (1996).A Yield Factor Model of Interest Rates, Mathematical Finance 6, 379–406. Hull J., White A. (1990).Pricing Interest–Rate Derivative Securities, The Review of Financial Studies 3, 573–592. Oksendal B. (1995).Stochastic Differential Equations, Springer–Verlag Berlin Heidelberg. Tauchen G. (1986).Finite–State Markov Chain Approximation to Univariate and Vector Autoregressions, Economic Letters, 20, (1986), 177–181. Tauchen G., Hussey R. (1991).Quadrature–Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models, Econometrica, Vol. 59, No. 2 (Mar. 1991), 371–396. Vasicek O. (1977).An Equilibrium Characterization of the Term Structure, Journal of Financial Economics 5, 177–188. Wilkie A.D. (1986).A Stochastic Investment Model for Actuarial Use, Transactions of the Faculty of Actuaries 39, 341–403. Wilkie A.D. (1995).More on a Stochastic Investment Model for Actuarial Use, British Actuarial Journal 1, no. 5:777–964. 12 � Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Extent The size or duration of the resource. 1578 Title A name given to the resource A Model for Discrete Time/Space Approximation of the Vasicek Model for the Interest Rate Author Author GAVRANOVIĆ, Nedim Abstract A summary of the resource. In this paper we present the mathematical model for the real interest rate as an autoregressive discrete time and discrete state space process. The process is an approximation of Vasicek continuous time–space autoregressive process presented in Vasicek (1977). We choose Vasicek model for interest rate for developing bond prices as the one which is used in the analysis of optimal asset allocation problems by many authors. It is a type of one factor short rate model where interest rate movements are driven by one source of market risk. Our model can be used in many applications when modelling an interest rate mathematically or for making simulations on the computer. The shortcoming of Vasicek model is the positive probability of the negative value of interest rate. Due to mean reverting characteristic of the interest rate, even for the negative value of real interest rate, there will be a certain demand for both traditional and index–linked bonds. It is possible to derive the bond market model using the interest rate which does not allow the negative values of the interest rate, for example Cox–Ingersoll–Ross model (Cox et al (1985)). Although CIR model may be more appropriate, and the one and ten years rolling bonds market model can be developed using CIR model, it would be also computationally more demanding. In our model we assume that the discrete time interval is one year. We will show below the technique to transform the continuous time Vasicek process into a discrete time one. We assume that the interest rate can take a finite number of values in a reasonable range. As the Vasicek process transformed into discrete time is still a continuous state space process we use the technique from Tauchen and Hussey (1991) and as a result we get a process with discrete time–state space. Once we obtain a discrete time–state process for real interest rate we can model bond prices as the expected present value of future incomes from the bond. As we assume a zero coupon bond, it means that the bond price is expected present value of one money unit that will be due in n years’ time, where n years is the bond duration. Following the Vasicek approach, we can also introduce a market price of risk. As a final result we get the approximation of the bond market. Keywords: Discrete Time, the Vasicek Model, Interest Rate. Publisher An entity responsible for making the resource available International Burch University Date A point or period of time associated with an event in the lifecycle of the resource 2013-05-10 Keywords Keywords. Article PeerReviewed Identifier An unambiguous reference to the resource within a given context ISSN 978-9958-834-23-3 https://omeka.ibu.edu.ba/files/original/e376a1ff77b93475239920c2a8e36b8d.pdf 976f73d35841d8301000bf8c58f41235 PDF Text Text A Multilingual Media Monitoring System (MMMS) for Balkans B. Gültekin ÇETĐNER Faculty of Engineering and Natural Sciences International University of Sarajevo (IUS) Sarajevo, Bosnia and Herzegovina cetiner@ius.edu.ba Mete GÜNDOĞAN Faculty of Economics and Business Administration International University of Sarajevo (IUS) Sarajevo, Bosnia and Herzegovina mgundogan@ius.edu.ba Osman GÜRSOY Faculty of Engineering and Natural Sciences Researcher in Computer Engineering International University of Sarajevo (IUS) Sarajevo, Bosnia and Herzegovina ogursoy@ius.edu.ba Abstract: This paper describes a developed Multilingual Media Monitoring System (MMMS) software and reports how it may be utilized to effectively facilitate PR facilities at an academic institution in Balkans. There are many international charity projects of Turkey in Bosnia and Herzegovina (BiH). These institutes comprise the academics and businessmen both from Turkey and Bosnia. Due to major number of the stakeholders and students from Turkey and Bosnia as well as other different countries, and the mission of such an institution to become an international Balkan institution requires the establishment to perform PR facilities in Balkans effectively in a multinational and multilingual manner. Therefore, a software system called Multilingual Media Monitoring System (MMMS) was developed by the authors herein to manage the PR facilities more effectively by easing the collection, search and evaluation of the news in Balkan region and Turkey. The paper describes the system in detail. Keywords: Media Monitoring, PR, Information Technology, Content Analysis, Balkan Cooperation Introduction After the war, many internatinal educational institutions have been established in BiH. They have both academicians and students from about many different countries of which the majority is from Turkey and Bosnia. The decision of the establishments goes back to the start of the post-war period when Alija Izzetbegovic, the first president of the independent Bosnia and Herzegovina had made a call to Turkey to establish the good relations with Turkey and help the country to reestablish the economy and development. Educational curricular structures of these institutions are usually based on a flexible model to allow the interdisciplinary studies and program changes considerably easy. The inspiration of the educational models is based on the structuring of curriculum at advanced academic institutions by revising them according to needs of Bosnia and Herzegovina. The international structure and stakeholders of such institutions from different countries make it necessary to develop a multilingual effective news monitoring system for PR facilities in Balkan region and Turkey. Therefore, a project was developed during 2009 to ease the PR facilities of such an institution. The main purpose of the project was to collect the content in several languages (currently in English, Bosnian and Turkish), to categorize, evaluate and search this content by predefined staff in several roles. Collection of news and other content is made by usually editors and evaluated by commentators. The software project shortly called as PRNews is a Multilingual Media Monitoring System (MMMS) and described herein this paper in detail. Media Monitoring Systems 356 �Media Monitoring systems are used by modern organizations to collect information for more effective decisions and often strategic management purposes. The application of content analysis, linguistic, and information retrieval methodologies are the focal point of the discussion in media monitoring systems. Content analysis is described as a well-described systematic strategy of inquiry to the analyzed media content object, or in other words, to a communication text (Arıkan, 2009). From the very beginning of the research it must be described what is looked after. In this project, Arıkan attempts to deliver primary information on a content analysis project to analyze Turkish Media by computer assistance. He discusses the methodological, scientific and application problems and issues related to the project. Media monitoring can help demonstrate that political competitors and the public at large should have confidence in the media, electoral authorities and the government that is responsible for providing genuine elections. Shortcomings in media conduct can be identified through monitoring in time for corrective action. Abuse of the mass media’s power to affect voter choices also can be documented, which allows the population and the international community to appropriately characterize the true nature of the electoral process. More may be found regarding media monitoring for political purposes in (coliver and Patrick, 1994) and (Lange and Palmer, 1995). A Digital Media Monitoring project for Parliament was reported (Gilbert, 2005). An Electronic Media Monitoring Service (EMMS) was developed to allow Senators and Members to browse, search and view television and radio items on desktop PCs. In this system, news and current affairs items are recorded in Canberra by Parliamentary Library staff and published onto the EMMS web site for access by Senators and Members in Parliament House and their electorate offices. Using the system developed, media programs may be digitally captured, encoded and archived for retrieval and playback by the Library’s clients. A news media monitoring or media tracking system can be used to collect, evaluate and search certain content of news coverage for more effective PR in an organization. The content may be related to a subject, person or any organization and may be on a hardcopy magazine and newspaper, or in a digital form. The collected and evaluated content under different categories may then be sent to related bodies or searched online. The following sections describe a multilingual news media monitoring system developed by the authors. Multilingual Media Monitoring System (MMMS) The Multilingual Media Monitoring System (MMMS) described herein allows administrative staff to browse, search and view news items online. News and current affairs items are recorded at a centre by staff arranged as editors and administrators and published onto the MMMS web site for access by staff assigned as users. It is integrated into the institution's database which means that any staff or client may be assigned the tasks with predefined users. The Use-case diagram in Figure 1 shows the users as participants and their roles to be played in the MMMS system. Multilingual Media Monitoring System Add/Modify Users Editor Adm in Add Languages Add Categories Add/Modify New s Advisor Evaluate New s User Search «include» Rate Show New s Figure 1. Use-case Diagram for MMMS 357 �The Admin user has all rights to describe, add and user profiles and their permissions. Admin also may add additional languages and perform operations of all other users. Besides Admin user, there are 3 other users as Editor, Advisor and User. Editor may add categories and add/modify news. Editor user is a typical PR user who can collect, modify the news content. Advisor may add, modify and rate (evaluate) the news content similar to Editor. User is typically a manager who sees all the results in read-only form. He/she can search and see the content and its related ratings. The user may rate the content. The media monitoring service is highly useful and this project has involved technology and ready to be applied to any academic institution. Using the new technology, media contents for Balkan region are digitally captured, encoded and archived for retrieval and playback by the MMMS clients. The following part describes the project, the technology, standards employed, and how certain issues were overcome to provide an in-demand PR service for administrators. System Design for MMMS The MMMS developed herein is a web based software application using open source application development standards such as PHP programming language and MySQL as Database Management System. The data model for the designed database is given in Figure 2. Languages category notification Language Category_ID Description catName Notification_ID User_ID (FK) category keywords Language (FK) users media User_ID Media_ID title source author date summary keywords Category_ID (FK) Language (FK) Editor_User (FK) Comments comment_ID Comment Rating Media_ID (FK) Commentator_ID (FK) username password email name middlename surname lastlogin profile Figure 2. Data Model related to Database for MMMS The media content has title, source, author, date of information, summary, and keywords which are used to search later the media document. Each media content is categorized with related category ID. The PR user (editor or advisor) is also recorded as Editor User. Each Media content has also language associated with. User table is integrated into the Database of hosting institution. Therefore, new users from the academic and administrative personnel may be added to the user pool in MMMS easily. Comments may be given and ratings may be added by different users. Category table keeps all categories added into the system. Categories may be edited by both Admin and editor users. Currently there are 3 languages in the system but more languages may be added to the system. Notification is perhaps one of the most important tables in the system. Users are notified through their emails if there is a new media content in the system related to their category, keywords and language of interest. Users may also search inside the media content based on the filtering of language, keywords and category. User Interfaces for MMMS The user interfaces are many and difficult to show all herein. Therefore, only several important ones are described in this section. User interfaces are related to the Cases given in Figure 1. The participants are given different permissions according to their roles. The Figure 3 shows menu options for users with the roles Admin, Editor and User. The Admin user has permission to add/modify users whereas editor cannot change the users but can add News and Categories. The normal user has only read-only permission to search and see the news. The users can manage the CRUD (Create/Retrieve/Update/Delete) operations depending on their security levels. The users may be added by administrators with different privileges depending on the role of the user selected from 358 �the human resources associated with the institution’s database for employees. The alternative usage of the system may involve people from different organizations in Balkan region and Turkey to monitor the news media for research and other purposes. In this case, the actors described in Figure 1 may be distributed throughout the countries. For example, advisors from Istanbul may rate the content produced by an editor in Albania and users of Kosovo may see the content related to Kosovo produced by Istanbul editors etc. This kind of usage of the system requires a network of users from different countries with different roles. Figure 3. Menu Options for (a) Admin (b) Editor, and (c) User The most important part of the system is the search facility as shown in the left side of Figure 4 which shows the screenshot to be seen by admins, advisors, editors and users. The right part in the figure may be seen by only admins, advisors and editors. It contains a pool of the news produced mainly by editors. The search mechanism contains certain criteria for search and sort facilities. Filtering is available for category, language, search keywords and dates. Search is made on the html content based on the OR function of Boolean algebra. The html content may include pictures and videos. However, the system cannot search for information yet in binary content such as videos and pictures. The html results related to content are brough to the user as pdf files. Editing of the content is made over html. Sorting is possible based on the Title, Source of Information, Author, Category and Date. Editing of the content is possible via related functions. Although rarely used deletion of a content is also possible. This may be an option to be used by editors and advisors if the content’s rating and evaluation require so. Currently system does not allow the users to share selected content via sending through emails. A workflow management system may also be added in future versions to accept content in a hierarchical manner. This means approval of content by advisors and certain editors. Currently system is very useful for copying and pasting digital information from digital soft copies related to events. For facilitating hard copy information, the editor needs to scan and convert the hardcopy contents (such as newspaper, leaflet etc) manually to soft copy formats through Optical Character regognition (OCR) softwares. 359 �Figure 4. A typical screen to be seen by editors Conclusions The paper has described a Multilingual Media Monitoring System (MMMS) developed by the authors for the purpose of tracking the media for news content of both Balkan region and Turkey related to the conduct of PR facilities at any educational institution. The main purpose was to provide up-to-date information needed by the managers of the institution to help in their decision making processes for more effective PR. It was found useful by higher level managers in tracking the news in three different languages. The system may be utilized in a way to monitor the information gathering throughout the Balkan region by embedding editorial board members and advisors from different countries. The system is ready to be operated by any educational or academic institutions as well as any governmental institutions. References Arikan, Aykut (2009), “Computer Assisted Turkish Based Media Content Analysis System - Project 107k209: A Case Study“, Bilgi Dünyasi, 10 (2) Coliver, Sandra And Patrick Merloe (1994) “Guidelines For Election Broadcasting In Transitional Democracies”, United Kingdom, Article 19, National Democratic Institute For International Affairs Lange, Yasha And Palmer, Andrew (1995) “Media And Elections: A Handbook”, European Institute For Media, Brussels:Tacis Gilbert, Catherine (2005) “Digital Media Monitoring Project For Parliament”, 12th Information Online Conference, Sydney, 1-3 February, Australia 360 � Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Extent The size or duration of the resource. 527 Title A name given to the resource A Multilingual Media Monitoring System (MMMS) for Balkans Author Author ÇETİNER, B. Gültekin GÜNDOĞAN, Mete GÜRSOY, Osman Abstract A summary of the resource. This paper describes a developed Multilingual Media Monitoring System (MMMS) software and reports how it may be utilized to effectively facilitate PR facilities at an academic institution in Balkans. There are many international charity projects of Turkey in Bosnia and Herzegovina (BiH). These institutes comprise the academics and businessmen both from Turkey and Bosnia. Due to major number of the stakeholders and students from Turkey and Bosnia as well as other different countries, and the mission of such an institution to become an international Balkan institution requires the establishment to perform PR facilities in Balkans effectively in a multinational and multilingual manner. Therefore, a software system called Multilingual Media Monitoring System (MMMS) was developed by the authors herein to manage the PR facilities more effectively by easing the collection, search and evaluation of the news in Balkan region and Turkey. The paper describes the system in detail. Date A point or period of time associated with an event in the lifecycle of the resource 2010-06 Keywords Keywords. Conference or Workshop Item PeerReviewed Q Science (General) https://omeka.ibu.edu.ba/files/original/9e0c91b85bf61a9f0f7ec711d98ca63d.docx fa6d26f8319b99684a60eac66a01852b https://omeka.ibu.edu.ba/files/original/5448e1c797e85c05644cb4dd884f5d0e.pdf c28a78ff704165751e493f5e7b2f2fb9 PDF Text Text A National Quality Infrastructure Alma Aganović Institute of metrology of Bosnia and Herzegovina Bosnia And Herzegovina alma.aganovic@hotmail.com Abstract: Quality is the result of the integration and coordination of a series of activities in several interrelated subjects: metrology, standardization, testing, accreditation, and certification. The state is obliged to regulate aspects related to the valid system of measures, regulations and standards related to certain aspects of the environment, health and safety, as well as the responsibility of government authorities and private organizations on these issues. States with effective public structures within which are included many institutions dealing with infrastructure quality are in a better position to express the interests of their populations in terms of global policy and implementation of international regulations. Keywords: quality infrastructure, accreditation, standardization, certification, metrology. 182 � Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Extent The size or duration of the resource. 2661 Title A name given to the resource A National Quality Infrastructure Author Author AGANOVIĆ, Alma Abstract A summary of the resource. Quality is the result of the integration and coordination of a series of activities in several interrelated subjects: metrology, standardization, testing, accreditation, and certification. The state is obliged to regulate aspects related to the valid system of measures, regulations and standards related to certain aspects of the environment, health and safety, as well as the responsibility of government authorities and private organizations on these issues. States with effective public structures within which are included many institutions dealing with infrastructure quality are in a better position to express the interests of their populations in terms of global policy and implementation of international regulations. Keywords: quality infrastructure, accreditation, standardization, certification, metrology. Publisher An entity responsible for making the resource available International Burch University Date A point or period of time associated with an event in the lifecycle of the resource 2014-04 Keywords Keywords. Article PeerReviewed Identifier An unambiguous reference to the resource within a given context ISSN 2303-4564 H Social Sciences (General) https://omeka.ibu.edu.ba/files/original/d2ad00991f6bceb1e1a6dd009b852f1a.docx ef3982ab8da72bdb8a33151330fdacad https://omeka.ibu.edu.ba/files/original/6b230b639ddf357dc6e0222bb9a1eaf2.pdf 53b0034d613c6fea5e63fc39108507a6 PDF Text Text A National Quality Infrastructure Alma Aganović Institute of metrology of Bosnia and Herzegovina Bosnia And Herzegovina alma.aganovic@hotmail.com Abstract: Quality is the result of the integration and coordination of a series of activities in several interrelated subjects: metrology, standardization, testing, accreditation, and certification.The state is obliged to regulate aspects related to the valid system of measures, regulations and standards related to certain aspects of the environment, health and safety, as well as the responsibility of government authorities and private organizations on these issues.States with effective public structures within which are included many institutions dealing with infrastructure quality are in a better position to express the interests of their populations in terms of global policy and implementation of international regulations. Keywords: quality infrastructure, accreditation, standardization, certification, metrology. 182 � Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Extent The size or duration of the resource. 2669 Title A name given to the resource A National Quality Infrastructure Author Author AGANOVIĆ, Alma Abstract A summary of the resource. Quality is the result of the integration and coordination of a series of activities in several interrelated subjects: metrology, standardization, testing, accreditation, and certification. The state is obliged to regulate aspects related to the valid system of measures, regulations and standards related to certain aspects of the environment, health and safety, as well as the responsibility of government authorities and private organizations on these issues. States with effective public structures within which are included many institutions dealing with infrastructure quality are in a better position to express the interests of their populations in terms of global policy and implementation of international regulations. Keywords: quality infrastructure, accreditation, standardization, certification, metrology. Publisher An entity responsible for making the resource available International Burch University Date A point or period of time associated with an event in the lifecycle of the resource 2014-04 Keywords Keywords. Article PeerReviewed Identifier An unambiguous reference to the resource within a given context ISSN 2303-4564 H Social Sciences (General) Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Extent The size or duration of the resource. 800 Title A name given to the resource A Needs Assessment Study of a Language Preparatory Program in terms of the Students’ Reading and Writing Abilities Author Author Enisa, Mede Abstract A summary of the resource. A needs assessment study is usually carried out for different purposes. Collecting information on a specific problem that learners are experiencing, helping to determine if an existing course adequately addresses the needs of potential students, finding out the perceptions of related parties regarding the skills a learner needs in order to perform a specific role, demonstrating a change of direction that people in a reference group feel is important, and signifying a discrepancy between the perceptions about what the students are able to do and what they need to be able to do are the among the main reasons for needs assessments to be conducted (Brown, 1995; Richards, 2001). The aim of the present study is to identify the students’ perceived language needs in terms of their reading and writing abilities. A sample of forty-eight students and fifteen instructors enrolled in an English Preparatory Language Teaching program at a highly competitive private university in Istanbul, Turkey participated in the study. Data came from a needs analysis questionnaire and a semi-structured interview conducted with the two groups of partcipants. The findings suggested important implications for evaluating and redesigning the reading and writing syllabi for the following academic year. Date A point or period of time associated with an event in the lifecycle of the resource 2012-05 Keywords Keywords. Conference or Workshop Item PeerReviewed P Philology. Linguistics https://omeka.ibu.edu.ba/files/original/88a42195e6bbce14a3b8c80377a68fa2.pdf 91160412c4899bf99a4c0f45fd7f081b PDF Text Text 1st International Syposium on Sustainable Development, June 9-10 2009, Sarajevo A New Approach to a Marketing Decision Model via the Fuzzy Expert System A.Samet Hasiloglu Department of Computer Engineering, Ataturk University, Erzurum, Turkey, asamet@atauni.edu.tr U mit Gul Vocational College of Narman, Ataturk University, Erzurum, Turkey Abstract: This paper proposes a new forecasting method for a marketing decision model. To support the modeling process, a fuzzy expert system was designed to determine whether a new product should enter the market. The fuzzy expert system based model presenting of a new product to the market at the best time will provide an advantage to the companies in competitive environment and increase their share of the market. In the final stage of this framework, algorithms for building fuzzy expert systems are explained and applied to a case study. The proposed method was tested with an actual data load of product life cycle. Keyword: fuzzy expert system; product life cycle; marketing decision model Introduction Real-world decision-making is much too complex, uncertain and imprecise to lend itself to precise, prescriptive analysis.Itisthis realization that underlies the rapidly growing shiftfrom conventional techniques of decision analysis to technologies based on fuzzy logic. Fuzzy logic was originally proposed as a means of representing uncertainty and formalizing qualitative concepts that have no precise boundaries. So far, of fuzzy logic has gained much more attention in engineering applications than in business and finance applications, but an even larger potential existsinthe latterfields (Facchinetti et al., 2003 & Yavuz et al.). Fuzzy logic is an excellent way to combine Artificial Intelligence methods (Zadeh, 1993). Fuzzy set theory and fuzzy logic provide a general method for handling uncertain and vague information, which unfortunately are unavoidable in many real world decision-making processes (Frantti & Mahonen, 2001). Fuzzy logic avoids the abrupt change from one discrete output state to another when the input is changed only marginally. Thisis achieved by a quantization of variablesinto membership functions (Herrmann, 1995). Expert systems were designed to reason through knowledge to solve problems using the same methods that humans use. A fuzzy expert system is an expert system that utilizes fuzzy sets and fuzzy logic to overcome some ofthe problems which occur when the data provided by the user are vague orincomplete. In this paper, we illustratethatthe fuzzy approach may be usefulin industrial economics.In particular, a fuzzy expert system has been adapted for product life cycle management. The well-known product life cycle approach describes the changing features of markets during their evolution. It may therefore serve as a theoreticalframework within which market changes can be explained (Klepper & Graddy, 1990). To supportthe decision process, a fuzzy expert system was designed to determine whether to enter of a new product into the market. Finally, when operating the fuzzy expert system, three different deductions can be made:the preservation of the present status,the introduction ofthe new productto the market and the withdrawal of the productfrom the market. The organization of this paper is organized as follows: Section 2 briefly summarizes the basic principles ofthe productlife cycle. Section 3 provides an overview of the Fuzzy expertsystems.In section 4 (the main part of this paper),the major modeling issues ofthe study are examined, based on a fuzzy expert system. This paper concludes with a summary ofthe findings and directions for future research. 241 �1st International Syposium on Sustainable Development, June 9-10 2009, Sarajevo Product Life Cycle All products and services have certain life cycles. Life cycle refers to the period from the product’s first launch into the market untilits final withdrawal. The life cycleis split up in phases. Since an increase in profits isthe major goal of a company that introduces a product into a market,the product’s life cycle management is very important(Komninos, 2002). New product failures may occur because of an overestimation of market size, product design problems,Incorrectly positioned, priced or advertised products,costs of product development and / or competitive actions (Kotler & Armstrong, 2001). Although the life cycle varies in accordance with the product and sector base,the product’slife cycle – period usually consists of five major phases as shown in (Fig. 1). The first period is the product development phase, the second period is the entrance phase, the third period is the growth phase, the fourth period is the maturity phase and the fifth period is the satisfaction phase. The product development phase begins when a company finds and develops a new productidea. The entrance phase isthe period of a product’s presentation to the market and the effort spent for its acceptance. Generally, this isthe period of catching up at par point. The growth phase is the best step, where the product has reached its maximum profit and has been through its brightest period. In the maturity phase, problems gradually arise up and in sales startto decrease. Despite this sales decrease, companies try to keep their sales high by using other marketing activities,called sales efforts.In that period increase in sales like jumping sales (comb tooth) occur. It is generally agreed that innovation, performance, and competition depend significantly on the maturity ofthe markets(Dosi,1997). The Satisfaction phase isthe period thatthe companies prefer notto be in because they willstarttolose in a while. During the maturity period, significant changes are made in the way that the product is behaving in the market. Presentation of a new product to the market at the best time will provide an advantage to competing companies and increase their share ofthe market (Leenders & Wierenga, 2002). Figure 1: Life cycle period of a new product In the conventional productlife cycle,introduction of a new productto the market corresponds point "A" in (Fig. 1) (http://www.otterbein.edu/home/fac/brccbly/courses/images/plc.gif). When a company comes to this point atthe end of the maturity period, it has to choose one of these alternatives: new product, new market, or withdrawal of goods from the market,so as notto enterinto the 5-th period. As shown in Point "A" (McDonald, 1995)the existing system is considered to be lateforthe new product to enter the market. This point is the period in which the company withstands a number of costs called other sales efforts(promotion, excess goods, discount, etc.)to keep the sales active.Itis plain to see from a review of the conventionallife cycle that profit has started to fallin spite ofthe increase in sales. The proposed system attempts to determine the point specified as point "A" in (Fig. 1) by means of the expertsystem. Inthis proposed structure, point "A" can be taken to an earliertime than in the existing policies.In the operation ofthe system, productlife cycle maturity period characteristics will be reviewed and efforts will be made to determine the most suitable time for presentation ofthe productto the market by evaluating the factors called as macro and micro marketindicators. There are some major productlife cycle managementtechniques that can be used to optimize a product’s revenues in respect to its position in a market and its life cycle. These techniques are mainly marketing or management strategies that are used by most companies worldwide and include the know-how of product 242 �1st International Syposium on Sustainable Development, June 9-10 2009, Sarajevo upgrade,replacement and termination. Nevertheless, a product manager must know how to recognize which phase of itslife cycle a product is in,regardless ofthe problems inthe model discussed above. To do that,a good method is the one which follows (Komninos, 2002): a.Collection ofinformation aboutthe product’s behavior over a period atleast of 3–5 years. (Information willinclude price, units sold,profit margins,return ofinvestment – ROI, market share and value). b.Analysis of competitor short-term strategies (analysis of new products emerging into the market and competitor-announced plans about production increase, plant upgrade and product promotion). c.Analysis ofthe number of competitorsin respect of marketshare. d.Collection ofinformation ofthe life cycle of similar productsthat will help to estimate the life cycle of new products. e.Estimation of sales volume for 3 – 5 years from productlaunch. f.Estimation of the total costs compared to the total sales for 3 – 5 years after product launch (development, production, promotion costs). Strategies that must be applied as soon as the phase of product life cycle is recognized are given in the (Tab. 1) (Komninos, 2002). Strategic Goal Competition Product Development Phase Make your product known and establish a test period Almost not there Product Limited number of variations Price Goal High sales to middle men Promotion Goal Entrance Phase Growth Phase Acquire a strong market position Maintain your market position and build on it Early entry of aggressive competitors into the market Introduction of product variations and models Price and distribution channel pressure Aggressive price policy (decrease) for sales increase Creation of Reinforcement of public-market product awareness product and preference awareness Exclusive General and and selective reinforced distribution through distribution through all distribution certain channels available distribution channels and creation of high profit margins for middle men Maturity Phase Satisfaction Phase Defend market position from competitors and improve your product Establishment of competitive environment “Milk” all remaining profits from product Improvement – upgrade of product Price decrease Re-estimation of price policy Defensive price policy Variations and models that are not profitable are withdrawn Maintain price level for small profit Reinforcement of middle men Maintain loyal to Gradual decrease middle men General and reinforced distribution with good supply to the middle men but with low margins of profit for them General and reinforced distribution with good supply to the middle men but with low margins of profit for them Some competitors are already withdrawing Withdrawal from most channels of distribution except those used in the development phase Table 1: Strategies of each productlife cycle phase Fuzzy Expert Systems A fuzzy expertsystem is an expertsystem that utilizesfuzzy sets and fuzzy logicto overcome some of the problems which occur when the data provided by the user are vague and incomplete.Itconsists of a fuzzification module, an inference engine, a fuzzy rule base and a defuzzification module. The fuzzification module preprocesses the input values submitted to the fuzzy expert system. Crisp inputs x1 x2 . . . xn ... Fuzzification Subsystem Fuzzy Rule Base Fuzzy inference engine 243 �1st International Syposium on Sustainable Development, June 9-10 2009, Sarajevo Figure 2: Structure ofthe fuzzy expert system The inference engine usesthe results ofthe fuzzification module and accessesthe fuzzy rulesinthe fuzzy rule base to infer whatintermediate and output values to produce. The final output ofthe fuzzy expert system is provided by the defuzzification module. The structure of the developed system is shown in (Fig. 2). This structure is common for fuzzy inference systems. Developed Marketing Decision Model In this study, a new marketing decision model was developed, whose structure identifies the fuzzy logic inference flow from the input variablestothe output variables. The fuzzification inthe inputinterfacestranslates analog inputs into fuzzy values. The fuzzy inference takes place in rule blocks, which contain the linguistic control rules. The outputs of these rule blocks are linguistic variables. The defuzzification in the output interfaces translatesthem into analog variables. The decision tree ofthe modelis shown in (Fig. 3).   Economic _ conditions Global _ Market   Political _ Circums tan ces   Competition   Performance _ of _ productManufacture Other _ Selling _ Efforts  Pr oportional _ Increase _ ın _ Sells    Manufacture _ Po int T arg et _ Market   Re newal Figure 3: Decision tree ofthe model (Fig. 4) shows the entire structure of this fuzzy system including input interfaces,rule blocks and output interfaces. The connecting lines symbolize the data flow. The fuzzification method, “Compute membership function (MBF)”,isthe standard fuzzification method used in almost all applications. This method only storesthe definition points ofthe membership functions in the generated code and computes the fuzzification atruntime. For output variables, different defuzzification methods exist as well. The most often used method is center-of-maximum (“Co M”), which delivers the best compromise of the firing rules (Von Altrock, 1997; Bojadziev & Bojadziev, 1997). In (Fig. 4),the rule block ofthe structure ofthe fuzzy logic system is shown. This block containsthe rules of the system describing the control strategy. Rule blocks contain the control strategy of afuzzy logic system. 244 �1st International Syposium on Sustainable Development, June 9-10 2009, Sarajevo Figure 4: Structure ofthe fuzzy logic system Each rule block confines allthe rules for the same context. A context is defined by the same input and output variables of the rules. The ‘IF' part of the rules’ describe the situation for which the rules are designed. The ‘THEN’ part describes the response of the fuzzy system in this situation. The degree of support (DoS) is used to weigh each rule according to itsimportance, which ranges from zero to one. Global market indicators, overall economic situation and legal and political circumstances prevailing in the market arethe factors reviewed. The fuzzy expertrules of the global market can be sum marized in (Tab. 2). Economic cond. Negative Negative Negative Ineffective Ineffective Ineffective Positive Positive Positive IF AND Political circums. Negative Ineffective Positive Negative Ineffective Positive Negative Ineffective Positive THEN Global market Pessimistic Pessimistic Pessimistic Pessimistic Pessimistic Optimistic Pessimistic Optimistic Optimistic Table 2: Rules ofthe rule block “RuleBlockGlobalMarket” The target marketindicatorfactors are a renewal ofthe product and manufacture point. Manufacture point isthe comparison of performance of the products and itsrivals. The result of this review revealsthe probability that performance of the product can be lower or higher than or equal to that of the closest rival product. The condition of “manufacture point” has three condition domain factors: m.p. < c.m.p., m.p. = c.m.p.and m.p. > c.m.p. Above, “m.p.” is the manufacture point of our product, “c.m.p.” is the manufacture point of the competitor’s product. The Fuzzy expertrulesinthe target market are summarized in (Tab.3). IF Manufacture point AND Renewal THEN Target market Mp<cmp not_ok Wait Mp<cmp Mp=cmp Mp=cmp Mp>cmp Mp>cmp Ok not_ok Ok not_ok Ok Medium Wait Impulsive Medium Impulsive Table 3: Rules ofthe rule block “RuleBlockTargetMarket” The factors of manufacture indicators are “competition”, “other selling efforts” and “proportional increase in sales”. The most striking signs of the maturity stage are a decrease in competition, rivals’ introduction of new products to different market sector and construction of existing market. The fuzzy expert rules of “manufacture” can be summarized in production rules in (Tab. 4). 245 �1st International Syposium on Sustainable Development, June 9-10 2009, Sarajevo Competition Decreased Decreased Decreased Decreased Increased Increased Increased Increased AND IF Other selling efforts Decreased Decreased Increased Increased Decreased Decreased Increased Increased AND Prop. increase in sells Decreased Increased Decreased Increased Decreased Increased Decreased Increased THEN Manufacture Poor Good Good Very good Good Very good Very good Very good Table 4: Rules ofthe rule block “RuleBlockManufacture” As a result of a sales rates' decrease, a company willinitiate other sales efforts to increase sales. These efforts will escalate the cost of other sales efforts. Thus, the profit rate will drop because a big portion of the profitis used to finance other sales efforts. The fuzzy expertrules in the “Performance” can be summarized in the production rulesin (Tab. 5) and (Tab. 6) shows the summary ofthe project. Global market Pessimistic Pessimistic Pessimistic Pessimistic Pessimistic Pessimistic Pessimistic Pessimistic Pessimistic Optimistic Optimistic Optimistic Optimistic Optimistic Optimistic Optimistic Optimistic Optimistic AND IF Manufacture Poor Poor Poor Good Good Good Very good Very good Very good Poor Poor Poor Good Good Good Very good Very good Very good AND THEN Performance Bad Bad Passive Bad Passive Passive Passive Passive Active Passive Passive Active Passive Active Active Active Active Active Target market Wait Medium Impulsive Wait Medium Impulsive Wait Medium Impulsive Wait Medium Impulsive Wait Medium Impulsive Wait Medium Impulsive Table 5: Rules ofthe rule block “RuleBlockPerformance” Global Market Manufacture Target Market Performance Result Input Variables 2 3 2 7 7 Output Variables 1 1 1 1 1 Intermediate Variables 1 1 1 3 3 Rule Blocks 1 1 1 1 4 Rules 9 8 6 18 41 Membership Functions 6 7 5 3 21 Table 6: Summary of project As a result of operating the expert system, three different deductions can be made: preservation of the present status,introduction of a new producttothe market and the withdrawal ofthe productfrom the market,i.e.: If PERFOR M A NCE = Active Then “Preserve the present status” If PERFOR M A NCE = Passive Then “Introduce the new producttothe market” If PERFOR M A NCE = Bad Then “Withdraw the product from market” Results The fuzzy expert system-based marketing decision model, which defines the product life cycle, was implemented in an automated knowledge base. Our model was constructed using FuzzyTech as an expert system development tool for determining productlife cycle. The Productlife cycle maturity period characteristics were reviewed and efforts were made to determine whethertointroduce the productintothe market or not. As a result of operating the expert system, three different deductions can be made: “preservation of the present status”, “introduction ofthe new producttothe market” and “withdrawal ofthe productfrom the market”. 246 �1st International Syposium on Sustainable Development, June 9-10 2009, Sarajevo Conclusion In this paper, we propose a way to deal with product life cycle management. This new idea is to reproduce what fuzzy expert system does when they have to decide a new product’s market entering time. Values taken by these reviewed factors are interpreted by means of the fuzzy expert system and the best decision forthe company is made. As a result ofthe study,the most suitabletime forintroduction ofthe product to the market can be determined, instead of withstanding the costs of other sales efforts and losing profit or risking the loss of market share during the product's maturity period. In further research, to get a most realistic model,itis possible to add quantitative parameters to model such as production per unittime, wasting machine hours,labor hours,and raw material. Besides,to adapting this model to reallife, generalrules should be extended. For example,to define political circumstances of the target society, new rules set can be added to model. References Bojadziev, G., & Bojadziev, M. (1997). Fuzzy Logic for Business, Finance and Management, Singapore, World Scientific Publishing Co. Dosi, G. (1997). Industrial structures and dynamics: evidence, interpretations and puzzles. Industrial and Corporate Change, 6, 3–24. Facchinetti, G., Mastroleo, G., & Paba, S. (2003). A Fuzzy Approach to Empirical Identification of Industrial Districts. In Fuzzy Application Library/Business Applications/ Identification of Industrial Districts, on-line http://www.fuzzytech.com/e/district.html Frantti, T., & Mahonen, P. (2001). Fuzzy Logic-based forecasting model, Engineering Applications of Artificial Intelligence, 14, 189-201. Herrmann, C.S. (1995). A Hybrid Fuzzy-Neural Expert System For Diagnosis, In M. Kaufman, IJCAI, (pp. 494-501). Montreal, Canada: Darmstadt. Kasabov, N. K. (1996). Foundation of neural networks, fuzzy systems, and knowledge engineering. NY: MIT Press. Klepper, S., & Graddy, E. (1990). The evolution of new industries and the determinants of market structure. RAND Journal of Economics, 21(1), 27–44. Komninos, I. (2002). Product Life Cycle Management, on-line http://www.urenio.org/tools/en/Product_Life_Cycle_Management.pdf Kotler, P., & Armstrong, G. (2001). Principles of Marketing, NJ: Prentice-Hall. Leenders, M.A., & Wierenga, B. (2002). The effectiveness of different mechanisms for integrating marketing and R&D Mark. The Journal of Product Innovation Management, 19(4), 305-317. McDonald, M. (1995). Marketing Plans. How to prepare them: how to use them. Third Edition, Oxford: Butter worthHeinemann Ltd. Von Altrock, C. (1997). Fuzzy Logic and Neurofuzzy Applications in Business and Finance, NJ: Prentice Hall. Yavuz, U., Hasiloglu, A.S., Kaya, MD., Karcioğlu, R. ve Ersöz, S., “Developing a marketing decision model using a knowledge-based system”, Knowledge-Based Systems 18 (2-3), 125-129 (Apr 2005). Yen, V.C. (1999). Rule selection in fuzzy expert systems, Expert Systems with Applications, 16, 79-84. Zadeh, L.A. (1993). The role of fuzzy logic and soft computing in the conception and design intelligent systems. In E. P. Klement, & W. Slany, Fuzzy Logic in Artificial Intelligence, 8th Austrian Artificial Intelligence Conference, FLAI '93, (pp. 1). Linz, Austria: 695, Springer. 247 � Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Extent The size or duration of the resource. 470 Title A name given to the resource A New Approach to a Marketing Decision Model via the Fuzzy Expert System Author Author Hasiloglu, A.Samet Gul, Umit Abstract A summary of the resource. This paper proposes a new forecasting method for a marketing decision model. To support the modeling process, a fuzzy expert system was designed to determine whether a new product should enter the market. The fuzzy expert system based model presenting of a new product to the market at the best time will provide an advantage to the companies in competitive environment and increase their share of the market. In the final stage of this framework, algorithms for building fuzzy expert systems are explained and applied to a case study. The proposed method was tested with an actual data load of product life cycle. Date A point or period of time associated with an event in the lifecycle of the resource 2009-06 Keywords Keywords. Conference or Workshop Item PeerReviewed Q Science (General) https://omeka.ibu.edu.ba/files/original/c4b46f09faeb35677b9cea457f4ddd85.docx 54ddddfc0eb214802493729f53384f10 https://omeka.ibu.edu.ba/files/original/e6e93c1bea0c4a3a6a6862e8e82e3f9e.pdf ebcc83b6b395553b7b3b2ced29625796 PDF Text Text A NEW APPROACH TO WATER QUALITY TESTING FOR SUSTAINABLE WATERWAY MONITORING Lejla Ridanovic, Sanel Ridanovic Džemal Bijedić University of Mostar, Mostar, Bosnia and Herzegovina ABSTRACT Water is a basic requirement for survival of all living beings, and one of the most precious natural resources. Hence, as environmental standards in the world are becoming more demanding, the water quality issues hold a special significance. Potential water usage depends on its quality - the physical, chemical and biological composition and concentration of certain substances in the water. Water quality varies, as well as the criteria used to evaluate it. For Bosnia and Herzegovina, with its abundant water resources, the challenges of preserving surface water quality and the issues of water resources management are becoming increasingly pronounced. In this paper, the overall stream water quality was estimated by the Neretva Water Quality Index (NWQI). The grouping of selected quality parameters, each representing a specific impairment category, allows efficient and precise estimation of the overall quality of water. This simple and quick method is suitable for routine monitoring of water quality and can be conducted entirely on site. The composite index was calculated as the harmonic mean of analytical values of: water temperature, pH, electrical conductivity, oxygen saturation, nitrogen, total phosphorus, and faecal coliforms. These parameters, crucial for the assessment of water quality have been selected according to the major criteria of stream health, whilst taking into account the hydrological and climatic factors specific to the studied area. Analysis of environmental impacts on water quality in the Neretva River can serve as the basis for an accentuated need for implementation and management of monitoring programmes aimed at protection and sustainabiliy of waterways. NWQI allows the most impaired variable to make the largest impact on the value of the index, and takes into account the spatial and temporal differences that a variable will exert on the overall water quality. � Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Extent The size or duration of the resource. 2144 Title A name given to the resource A NEW APPROACH TO WATER QUALITY TESTING FOR SUSTAINABLE WATERWAY MONITORING Author Author RIDANOVIC, Lejla RIDANOVIC, Sanel Abstract A summary of the resource. Water is a basic requirement for survival of all living beings, and one of the most precious natural resources. Hence, as environmental standards in the world are becoming more demanding, the water quality issues hold a special significance. Potential water usage depends on its quality - the physical, chemical and biological composition and concentration of certain substances in the water. Water quality varies, as well as the criteria used to evaluate it. For Bosnia and Herzegovina, with its abundant water resources, the challenges of preserving surface water quality and the issues of water resources management are becoming increasingly pronounced. In this paper, the overall stream water quality was estimated by the Neretva Water Quality Index (NWQI). The grouping of selected quality parameters, each representing a specific impairment category, allows efficient and precise estimation of the overall quality of water. This simple and quick method is suitable for routine monitoring of water quality and can be conducted entirely on site. The composite index was calculated as the harmonic mean of analytical values of: water temperature, pH, electrical conductivity, oxygen saturation, nitrogen, total phosphorus, and faecal coliforms. These parameters, crucial for the assessment of water quality have been selected according to the major criteria of stream health, whilst taking into account the hydrological and climatic factors specific to the studied area. Analysis of environmental impacts on water quality in the Neretva River can serve as the basis for an accentuated need for implementation and management of monitoring programmes aimed at protection and sustainabiliy of waterways. NWQI allows the most impaired variable to make the largest impact on the value of the index, and takes into account the spatial and temporal differences that a variable will exert on the overall water quality. Publisher An entity responsible for making the resource available International Burch University Date A point or period of time associated with an event in the lifecycle of the resource 2013-05-24 Keywords Keywords. Article PeerReviewed Identifier An unambiguous reference to the resource within a given context ISSN 2233-1565 Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Extent The size or duration of the resource. 830 Title A name given to the resource A New Necessity in Foreign Language Teaching: Teaching Children a Second Language Author Author Savlı, Fusun Abstract A summary of the resource. Up until the 20th century, dissemination of English language by means of the colonies of England and the dominance of the United States of America resulted in the perception, acknowledgement and learning of English as the only language by millions of people. However, numerous studies have been conducted on the necessity of learning a foreign language in the last 30 to 40 years. Particularly resulting from the age of communication that our world experiences, and the insufficiency of speaking their own languages while different nations communicate with one another lead to the increase of the studies on foreign language teaching in number in recent years. The most significant aim of these studies is to promote the cooperation between the members of the European Union in any field. For that matter, the European Union raised the consciousness of a multilingual and multicultural European citizenship in order to ensure the protection and learning of different languages and cultures making up the richness of Europe. Accordingly, it laid down the educational policy of the European Union which is in force in many European countries. One of the issues on which the most numerous studies have been carried out is the “early teaching of foreign language”. In this presentation, we aim at answering such questions as what early teaching of foreign language is, why it is important and how it should be ensured, with special reference to the approaches to be taken into consideration and linguistic skills to be acquired during the early teaching of foreign language after touching upon the policies of foreign language being implemented in the European Union and in Turkey. In addition, we shall offer some suggestions on the actions to be taken in order to render this process more efficient for children and to improve their success. Date A point or period of time associated with an event in the lifecycle of the resource 2012-05 Keywords Keywords. Conference or Workshop Item PeerReviewed P Philology. Linguistics https://omeka.ibu.edu.ba/files/original/7aa1cac0ebfe68bc67b71deb439edb3f.docx 53dc6e157b5950bc975bcdf384f748fd https://omeka.ibu.edu.ba/files/original/45860662c54475b3dd9914f9c1c71d1d.pdf b55c521b1491cc9cf7f3c072bc571461 PDF Text Text Keynote Speaker A New Understanding of Linguistic Competence Diane Larsen-Freeman University of Michigan/ Michigan, USA ABSTRACT In this talk I will argue that our notion of linguistic competence needs to be revisited. Static depictions of the grammar of the target language are not suitable for informing research and language teaching. The fact is that language is dynamic, a characteristic that the term “competence” does not reflect. By entertaining a view of language informed by Complexity Theory, we will come to see language as a complex adaptive system. Complexity theory sees language as a set of patterns emerging from use. Those that are frequently-occurring become emergent stabilities in a complex system. The patterns themselves are variegated in form, and their borders are graded, not discrete.Complexity theorists subscribe to an emergentist view of language development. As such, no innate language acquisition faculty is posited. Instead, it is thought that a learner’s language resources develop from the interactions that the learner experiences. Out of these interactions, a new order self-organizes. Development is thus never complete, and a learner’s language resources can be seen as a dynamic ensemble of interacting patterns. � Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Extent The size or duration of the resource. 1716 Title A name given to the resource A New Understanding of Linguistic Competence Author Author LARSEN-FREEMAN, Diane Abstract A summary of the resource. In this talk I will argue that our notion of linguistic competence needs to be revisited. Static depictions of the grammar of the target language are not suitable for informing research and language teaching. The fact is that language is dynamic, a characteristic that the term “competence” does not reflect. By entertaining a view of language informed by Complexity Theory, we will come to see language as a complex adaptive system. Complexity theory sees language as a set of patterns emerging from use. Those that are frequently-occurring become emergent stabilities in a complex system. The patterns themselves are variegated in form, and their borders are graded, not discrete.Complexity theorists subscribe to an emergentist view of language development. As such, no innate language acquisition faculty is posited. Instead, it is thought that a learner’s language resources develop from the interactions that the learner experiences. Out of these interactions, a new order self-organizes. Development is thus never complete, and a learner’s language resources can be seen as a dynamic ensemble of interacting patterns. Publisher An entity responsible for making the resource available IBU Publishing Date A point or period of time associated with an event in the lifecycle of the resource 2013-05-03 Keywords Keywords. Article PeerReviewed Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Extent The size or duration of the resource. 3570 Title A name given to the resource A New Understanding of Linguistic Competence Author Author LARSEN-FREEMAN, Diane Abstract A summary of the resource. In this talk I will argue that our notion of linguistic competence needs to be revisited. Static depictions of the grammar of the target language are not suitable for informing research and language teaching. The fact is that language is dynamic, a characteristic that the term “competence” does not reflect. By entertaining a view of language informed by Complexity Theory, we will come to see language as a complex adaptive system. Complexity theory sees language as a set of patterns emerging from use. Those that are frequentlyoccurring become emergent stabilities in a complex system. The patterns themselves are variegated in form, and their borders are graded, not discrete.Complexity theorists subscribe to an emergentist view of language development. As such, no innate language acquisition faculty is posited. Instead, it is thought that a learner’s language resources develop from the interactions that the learner experiences. Out of these interactions, a new order self-organizes. Development is thus never complete, and a learner’s language resources can be seen as a dynamic ensemble of interacting patterns. Date A point or period of time associated with an event in the lifecycle of the resource 2013 Keywords Keywords. Conference or Workshop Item PeerReviewed PE English