The paper overviews stochastic optimization models of insurance mathematics and methods for their solution from the point of view of stochastic programming and stochastic optimal control methodology, with vector optimality criteria. The evolution of an insurance company’s capital is considered in discrete time. The main random variables, which influence this evolution, are levels of payments, i.e. the ratios of paid claims to the corresponding premiums, per unit of time. The main decision variables are the structure of the insurance portfolio (the structure of the total premium) and the dividend payments. As for efficiency criteria, indicators of profitability are taken, and, as risk criteria, the probability of ruin or the recourse capital is used. The goal of optimization is to build efficiency frontiers and to find out Pareto-optimal solutions. Methods for solving these tasks are proposed.
Preprint, 12.10.2019. V.M.Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine. October 2019. To appear in "Cybernetics and Systems Analysis", Vol. 56(1).