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Stochastic optimal control of risk processes with Lipschitz payoff functions. (English. Russian original) Zbl 1308.93229

Cybern. Syst. Anal. 50, No. 5, 774-787 (2014); translation from Kibern. Sist. Anal. No. 5, 139-154 (2014).
Summary: 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.

MSC:

93E20 Optimal stochastic control
91B30 Risk theory, insurance (MSC2010)
91B38 Production theory, theory of the firm
93C55 Discrete-time control/observation systems
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