Abstract
This work develops asymptotically optimal dividend policies to maximize the expected present value of dividends until ruin. Compound Poisson processes with regime switching are used to model the surplus and the switching (a continuous-time controlled Markov chain) represents random environment and other economic conditions. Assuming the switching to be fast varying together with suitable conditions, it is shown that the system has a limit that is an average with respect to the invariant measure of a related Markov chain. Under simple conditions, the optimal policy of the limit dividend strategy is a threshold policy. Using the optimal policy of the limit system as a guide, feedback control for the original surplus is then developed. It is demonstrated that the constructed dividend policy is asymptotically optimal.
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