Optimal Proportional Reinsurance Policy Based on Regulations
ZENG Yan(1), LI Zhongfei(2)
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(1)School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275;(2)Lingnan (University) College, Sun Yat-sen University, Guangzhou 510275.
According to regulations, an insurance company must convert a certain level of reserve. In view of this, the insurer must keep its surplus no less than this reserve level. In this paper, the ``\,ruin\,'' time is defined as the first time to achieve the reserve level, and the target is to minimize the ``ruin'' probability of the insurer. It is assumed that the surplus process is described by a diffusion model, the insurer can purchase proportional reinsurance and its surplus is appreciated according to continuous compound interest with a constant force of interest. By using the stochastic dynamic programming approach, explicit expressions of the optimal value function and the optimal proportional reinsurance policy are obtained via solving the corresponding HJB equation. Finally, some economical explanations and a numerical example are provided.
ZENG Yan
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Optimal Proportional Reinsurance Policy Based on Regulations. Journal of Systems Science and Mathematical Sciences, 2009, 29(11): 1496-1506 https://doi.org/10.12341/jssms08480
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