Journal
ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES
Volume 30, Issue 3, Pages 721-734Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s10255-014-0414-8
Keywords
optimal dividend; risk constraint; classical risk model; fixed transaction cost
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Funding
- National Natural Science Foundation of China [71231008, 71201173, 71301031]
- Natural Science Foundation of Guangdong Province of China [S2012040006838]
- High-level Talent Project of Guangdong Research on Models and Strategies for Optimal Reinsurance, Investment and Dividend
- Post-Doctoral Foundation of China [2012M510195]
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In this paper we consider the problem of maximizing the total discounted utility of dividend payments for a Cramer-Lundberg risk model subject to both proportional and fixed transaction costs. We assume that dividend payments are prohibited unless the surplus of insurance company has reached a level b. Given fixed level b, we derive a integro-differential equation satisfied by the value function. By solving this equation we obtain the analytical solutions of the value function and the optimal dividend strategy when claims are exponentially distributed. Finally we show how the threshold b can be determined so that the expected ruin time is not less than some T. Also, numerical examples are presented to illustrate our results.
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