Abstract—In economic and finance, function of modelling and optimization is substantial. In fact, by using modelling we can implement, analyze, and control different theories of economic and finance in the market. Bank’s asset and liability management is one of the most important areas of study in finance. In this structure, bank’s asset and liability portfolio including lending, bonds and received deposit is optimized by expressing objective and constraint regarding different contract positions. In this paper, the application of Operation Research in the structure of modelling and optimization of bank’s asset and liability management is so obvious. In fact, it is an instrument to find the highest level of utility. In this research, we start with defining the concept of special finance ratio in bank’s balance sheet, then we consider notation for any decision variable. With due attention to these definitions, we wrote ratio in the form of mathematics formula and this is of importance in the body of this paper; and its distinction from other researches is the using of financial ratio for optimization. In the construction of this ratio formulation, some ratio are objectives and others are constraints guiding us to find mathematical programming and then to optimize it. In the construction of this formulation, there are absolute phrases and some objectives with goal, so we have goal fractional multi-objectives problems that in the part of the solving method of the paper, we present a method by change of variables. After solving this problem, we design bank’s behavioral policies and/or we can compare the optimized state with what has happened.
Index Terms—Modelling and optimization, fractional programming, goal programming, Asset and liability management.
Seyed Mohammad Esmaeil Pourmohammad Azizi is with the graduate of financial mathematics, Department of mathematics, Allameh Tabataba’i University (ATU), Tehran, Iran (e-mail: e.azizi@atu.ac.ir).
Abdolsadeh Neisy is with the faculty of Financial Mathematics, Department of mathematics, Allameh Tabataba’i University (ATU), Tehran, Iran (e-mail: a_neisy@atu.ac.ir).
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Cite: Seyed Mohammad Esmaeil Pourmohammad Azizi, and Abdolsadeh Neisy, "Mathematic Modelling and Optimization of Bank Asset and Liability by Using Fractional Goal Programing Approach," International Journal of Modeling and Optimization vol. 7, no. 2, pp. 85-91, 2017.
