A bank liquidity management under random oscillations of interest rates

The mathematical model of management of liquidity of bank have been built. The economy rate of growth is considered to be constant, while interest rates of short instruments osculates randomly. It is supposed, that the bank maximizes the expected net present value. The concept of optimal strategy of bank is entered. It is shown, that optimal strategy should satisfy Bellman equation. Solution of the equation is found in an explicit form. Various strategies of bank are considered depending on how the income of bank depends on random values.