Abstract
This paper studies the optimal dividend problem in the diffusion model with stochastic return on investments. The insurance company invests its surplus in a financial market. More specially, the authors consider the case of investment in a Black-Scholes market with risky asset such as stock. The classical problem is to find the optimal dividend payment strategy that maximizes the expectation of discounted dividend payment until ruin. Motivated by the idea of Thonhauser and Albrecher (2007), we take the lifetime of the controlled risk process into account, that is, the value function considers both the expectation of discounted dividend payment and the time value of ruin. The authors conclude that the optimal dividend strategy is a barrier strategy for the unbounded dividend payment case and is of threshold type for the bounded dividend payment case.
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This work is supported by the National Basic Research Program of China (973 Program) under Grant No. 2007CB814905 and the National Natural Science Foundation of China under Grant No. 10871102.
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Wang, W., Zhang, C. Optimal dividend strategies in the diffusion model with stochastic return on investments. J Syst Sci Complex 23, 1071–1085 (2010). https://doi.org/10.1007/s11424-010-8077-x
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DOI: https://doi.org/10.1007/s11424-010-8077-x