MATHEMATICAL MODEL OF THE BANKING FIRM AS TOOL FOR ANALYSIS, MANAGEMENT AND LEARNING

Abstract

     A bank is rather a complex system. It is caused by a considerable number of financial flows and the funds, having a various dynamic and probabilistic characteristics. Stable functioning of the system is provided due to hierarchy, external (prudential supervision) and internal regulators and restrictions, and feedbacks.
     One of the problem solved by models ALM is management of various risks (especially credit risk and interest-rate risk), including the problem of default probability decrease.
     The approach to mathematical modeling of cash flow accounts in assets and liabilities of the commercial bank based on the partial differential equations is novel and has no analogues in the literature. At the same time, the given approach is quite logic as reflects process of change of actives simultaneously in time and on "age". Depending on concrete theoretical or practical problems the given approach can be realized in the various modifications, two of which are presented in this paper.