Abstract. A general mathematical concept is proposed to describe bank operation. To this end, a reference model of bank operation is introduced, which describes evolution of capital by a Markov process. The ruin probability in the reference model that majorizes the probability of bank bankruptcy in the proposed model is estimated. The value of the initial bank capital such that the bank can operate for infinite time with a sufficiently small ruin probability is indicated.

Keywords: bank ruin probability, bank capital, investment strategy, strategy for attracting deposits, random variable, Markov chain.