| 索赔次数为复合Poisson-Geometric过程下的破产概率和最优投资和再保险策略 |
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| 引用本文： | 林祥,李娜.索赔次数为复合Poisson-Geometric过程下的破产概率和最优投资和再保险策略[J].应用数学,2011,24(1). |
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| 作者姓名： | 林祥 李娜 |
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| 作者单位： | 中南大学数学学院概率统计研究所,湖南长沙,410075 |
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| 基金项目： | 国家自然科学基金资助项目(10771216) |
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| 摘 要： | 本文对索赔次数为复合Poisson-Geometric过程的风险模型,在保险公司的盈余可以投资于风险资产,以及索赔购买比例再保险的策略下,研究使得破产概率最小的最优投资和再保险策略.通过求解相应的Hamilton-Jacobi-Bellman方程,得到使得破产概率最小的最优投资和比例再保险策略,以及最小破产概率的显示表达式.
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| 关 键 词： | 复合Poisson-Geometric过程 破产概率 投资 比例再保险 Hamilton-Jaco-bi-Bellman方程 |
Ruin Probability and Optimal Investment and Reinsurance Strategy for Insurer with Compound Poisson-Geometric Risk Process |
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| LIN Xiang,LI Na.Ruin Probability and Optimal Investment and Reinsurance Strategy for Insurer with Compound Poisson-Geometric Risk Process[J].Mathematica Applicata,2011,24(1). |
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| Authors: | LIN Xiang LI Na |
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| Institution: | LIN Xiang,LI Na(Institute of Probability & Statistics,School of Mathematics,Central South University Changsha 410075,China) |
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| Abstract: | In this paper,we consider an insurance company whose surplus (reserve) is modeled by a compound Poisson-Geometric risk process perturbed by a diffusion.The insurance company can invest part of the surplus in a risky asset and purchase proportional reinsurance for claims.We consider the optimization problem of minimizing the probability of ruin.By solving the corresponding Hamilton-Jacobi-Bellman equations,explicit expressions for the minimal ruin probability and the corresponding optimal strategies are obta... |
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| Keywords: | Compound Poisson-Geometric process Ruin probability Proportional reinsurance Investment Hamilton-Jacobi-Bellman equation |
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