Abstract. The paper studies stochastic optimal control problems for finding optimal dividend policies of an insurance company in discrete time and with general Lipschitz payoff functions, involving indicators of profitability and risk. To construct positional optimal controls and to evaluate performance indicators, the dynamic programming method is validated. The rate of convergence of the successive approximation method for finding generally unbounded Bellman functions is estimated. The Pareto-optimal set of the problem is numerically approximated by so-called barrier-proportional control strategies.

Keywords: risk process, insurance, stochastic optimal control, discrete time, Lipschitz payoff function, optimal dividend policy, dynamic programming, successive approximation method, Pareto optimality, barrier-proportional strategy.