Optimal control of risk process in a regime-switching environment

Details Optimal control of risk process in a regime-switching environment Optimal control of risk process in a regime-switching environment

2010-09-16

arxiv.org/abs/1009.3247v3

Mathematics

Optimization and Control

Keywords: Regime switching diffusion, continuity of the value function, exit time control, viscosity solution

Scientific paper

This paper is concerned with cost optimization of an insurance company. The surplus of the insurance company is modeled by a controlled regime switching diffusion, where the regime switching mechanism provides the fluctuations of the random environment. The goal is to find an optimal control that minimizes the total cost up to a stochastic exit time. A weaker sufficient condition than that of (Fleming and Soner 2006, Section V.2) for the continuity of the value function is obtained. Further, the value function is shown to be a viscosity solution of a Hamilton-Jacobian-Bellman equation.

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