Asymptotically Optimal Dividend Policy for Regime-Switching Compound Poisson Models

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.