Modelling Strategy of Loan and Deposit Activity of a Commercial Bank

The article considers development of strategy of loan-deposit strategy of a bank, which could be presented by relevant rates. Bank activity is described with goodwill and liquidity indicators that characterise tangible and intangible resources of an institution. Goodwill indicator is calculated on the basis of the previous period data. Liquidity is a relation of assets to liabilities at a certain moment of time. On the basis of these indicators the article develops a mathematical model, which includes an assumption about dependence of the rate of growth of deposits on liquidity and goodwill functions. There is a task of two criteria optimisation, the solution of which is a set of rates. The article considers cases when a bank does not change rates during a set period of time and when a bank changes them frequently under condition that rates are independent from each other. If we make an assumption that each change of rates is accompanied with costs, which are not reflected in the model, changing rates is inexpedient. The article offers to use partially constant average values of rates. The article considers the use of the ideal point for selection of one value out of the set of Pareto efficient solutions. Using presentation of the task of one criterion optimisation with respect to the liquidity ratio, the article shows that the use of the goodwill indicator influences the rate of growth of deposits. This task is a special case of the previous one, which means that this solution is within the set of the presented Pareto efficient point. But in the event of non-strict correspondence with the extreme value of the liquidity ratio, the solution worsens. The necessity of use of both criteria is important and improves the south for solution.