ABSTRAKT

The two-criteria problem of stochastic optimal control of the dividend policy of an insurance company with the profitability and risk indicators is studied. The evolution of the company's capital is modeled by a stochastic risk process in discrete time with subtraction of dividends. The average total discounted dividends are used as a measure of profitability, and the loan capital necessary to prevent the ruin, as well as the probability of achieving a negative value of the equity, are used as an indicator of risk. The problem is reduced to the one-criterion one using the penalty functions of risk. To find the optimal controls the method of dynamic programming is justified. The Bellman optimality equation is solved by the successive approximations method, which in this case has an exponential rate of the uniform convergence.