Asymptotically optimal dividend policy for regime-switching compound Poisson models |
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Authors: | G Yin Zhuo Jin Hailiang Yang |
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Institution: | 1. Department of Mathematics, Wayne State University, Detroit, Michigan, 48202, USA 2. Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong, China
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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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Keywords: | Asymptotic optimality compound Poisson model dividend policy regime switching |
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