Norkin B. Numerical methods for solving stochastic optimization problems in insurance mathematics.

The thesis is devoted to the development of numerical methods of actuarial mathematics, namely, numerical methods for solution of stochastic multiobjective op-timization problems and for risk assessment in insurance. As insurance business models the controlled stochastic risk processes are used, which model stochastic evolution of capital and reserves of an insurance company. As yield criteria expected discounted dividends, the expected discounted capital at the end of the planning peri-od, dispersion and quantiles of these values and others are used. As the risk indicators ruin probability, the expected lifetime of the risk process, borrowed capital necessary to prevent the ruin, the amount of the debt at the time of ruin, and others are em-ployed. In this paper we developed numerical methods for solving the following tasks: (a) the solution of integral equations of insurance mathematics, which specify the ruin probability as a function of the initial capital; (b) the solution of multiobjec-tive stochastic programming problems, arising in insurance applications; (c) solution of multicriteria stochastic optimal control problems for optimal governing a risk process. The main practical result of the thesis is development of a parallel information technology and software for solution of multiobjective stochastic optimization problems and risk assessment in insurance.