Asymptotically Optimal Dividend Policy for Regime-Switching Compound Poisson Models  

作　　者：G.Yin Zhuo Jin Hailiang Yang 

机构地区：[1]Department of Mathematics,Wayne State University,Detroit,Michigan 48202,U.S.A [2]Department of Statistics and Actuarial Science,The University of Hong Kong,Hong Kong

出　　处：《Acta Mathematicae Applicatae Sinica》2010年第4期529-542,共14页应用数学学报（英文版）

基　　金：supported in part by the National Science Foundation under DMS-0907753;supported in part by the National Natural Science Foundation of China (No.70871055);supported in part by the National Science Foundation under DMS-0603287;supported in part by Research Grants Council of HKSAR (Project No:HKU706209P)

摘　　要：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.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.

关 键 词：Asymptotic optimality compound Poisson model dividend policy regime switching 

分 类 号：O174.41[理学—数学] P315.5[理学—基础数学]