Stochastic Optimal Control of Risk Processes with Lipschitz Payoff Functions

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