The central issue of bank management is obtaining maximum yield while complying with prudential supervision requirements to reliability and good standing. Particular attention should be given to liquidity risks, whose fully-fledged analysis and management require to approach the bank as a dynamic system. The developed mathematical model includes three asset components (loans; bonds and another low risk securities; liquid assets – accounts, reserves, cash) and two liabilities components (equity and borrowed capital – deposits). Main management parameters of the bank’s balance sheet that support choosing adequate combination of returns and liquidity risk include turnover times of the loan portfolio and the securities portfolio, loan and deposit rates, the cash reserve ratio. This approach allows to clearly describe the transformation mechanism of core cash flows and formalize various rules of assets and liabilities management. The findings include analytical expressions allowing to research the impact of main constraints on the bank’s yield. Computer-aided implementation of this model may be used for computational studies of dynamics of balance sheet items and efficiency of different algorithms of asset placement decision-making.