Recently it's obvious that the banking business has become more complicated due to speedy technological expansion, development of economies, diversity of banking operations, and increasing competition between financial institutions, hence success of a bank depends on its asset and liability management quality, particularly in the unstable economical environments (Oguzsoy and Guven, 1996).
According to Kosmidou and Zopounidis (2002) Asset and liability management is one of the most important concerns in the strategic planning of any bank, and they define it as "simultaneous planning of all asset and liability positions on the bank's balance sheet under consideration of the different bank management objectives and legal, managerial and market constraints, or the purpose of mitigating interest rate risk, providing liquidity and enhancing the value of the bank".
Banks faces several and major threats like credit, liquidity, capital and interest rate risks (Oguzsoy and Guven, 1996) as well as other uncertainties in the future that may overcome on the financial and investments environment (Kosmidou and Zopounidis, 2002). All these threats have encouraged banks to look for an efficient way on how to manage their assets and liabilities, and this need has led banks to decide their optimal balance along with risk, liquidity and other uncertainties, taking into the consideration the main interactions among the structure of banks assets and liabilities, (Kusy and Ziemba, 1986).
For that reason, banks that operates in high and unstable inflationary environments are more sensitive to all types of risks mentioned above compared with banks operates in stable inflationary environments, due to high uncertainty in future business (Oguzsoy and Guven, 1996). As a result, banks and financial institutions must work hard to develop asset and liability management (ALM) tools, to measure the various risks they may face, and try to find the best option between the available and suitable methods and tools that could provide them with the most efficient ALM models ( Kosmidou and Zopounidis, 2007) .
A lot of studies have been concerned to develop and to improve the bank asset and liability management tools (Oguzsoy and Guven, 1996). Moreover "ALM models for banks should be created in line with the Basel II accord" (Mitra et.al, 2007). According to Mitra et.al (2007) mentioned in their paper that ALM model can be applied widely on banks, pension funds, insurance companies, hedge and mutual funds, university endowment funds and wealthy individuals, and all of these models were developed by writers and all the models worked effectively.
In reference to Oguzsoy and Guven (1996), ALM models can be either deterministic or stochastic, deterministic models use linear programming(LP), and one of the most efficient linear programming models on asset and liability management was developed by Chambers and Charnes (1961), this model led to a successful applications done by Cohen and Hammer(1967), Lifson and Blackman (1973), Moreover a multi-objective and LP model was developed for banks ALM to handle inconsistent objectives and this were done by Eatman and Sealy (1979) and Giokas and vassiloglou (1991) . On the other side there are the stochastic models which are used to optimize risk under uncertainty, and they have been used since the 1970's, and there are some important approaches on them, firstly the simulation models which are readily understood by bank managers, there is also the stochastic linear programming with simple recourse (SLPSR) in "which each realized random variables is handled by a constraint", another approach of stochastic modeling is derived from the theory of portfolio selection by Markowitz (1959), "where the risk is measured by variance in a single period planning horizon". In addition, as highlighted by Mitra et al. (2007) an important approach of stochastic modeling is the chance constrained programming which is firstly introduced by Charnes and Cooper in 1958, and according to Oguzsoy and Guven (1996) it was developed by Charnes and Thore (1966) and Charnes and Littlechild (1968).
Furthermore, from the revolutionary works on banks ALM model is Kusy and Ziemba (1986) where they introduced a multiperiod stochastic LP with SLPSR to manage the asset and liability and this model was employed on Vancouver City Savings Credit, and it was can be taken as a milestone among the models of ALM (Oguzsoy and Guven, 1996) . Another Stochastic multiperiod ALM model was developed by Oguzsoy and Guven on a Turkish bank to see the stochastic performance of uncontrollable variables (Oguzsoy and Guven, 1996), in the next section we will have a look at this model as an example to see how it works .
According to Kosmidou and Zopounidis (2007) ALM is depends a lot on the changing of markets interest rates, so a lot of models where developed regarding interest rate risks in order to evaluate and measure bank's interest rate risk, and the Gap analysis and duration methods, but there are limitations on using these methods, so in order to avoid this simulation models could be used to measure interest rate risks. Kosmidou and Zopounidis build up goal programming ALM model using simulation techniques, to let banks to manage their exposures to interest rate risks taking into consideration the Gap and duration methods. This model was applied on a commercial bank in Greece. Moreover, another methods concerning this issue, In their paper Derhmann et al. (2009) they derived a consistent and comprehensive simulation model to measure the riskiness correlated to bank's interest rate and credit risks, and by taking into the consideration the asset, liability and off balance sheet items pricing.
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