中山大学学报自然科学版 ›› 2012, Vol. 51 ›› Issue (1): 1-8.

• 研究论文 •    下一篇

带外生负债的保险公司最优再保险投资策略

李婵娟1,李仲飞2,3,曾 燕2   

  1. (1中山大学数学与计算科学学院,广东 广州 510275;2中山大学岭南学院,广东 广州 510275;3.中山大学管理学院,广东 广州 510275)
  • 收稿日期:2011-06-29 修回日期:1900-01-01 出版日期:2012-01-25 发布日期:2012-01-25
  • 通讯作者: 李仲飞

Optimal Reinsurance-Investment Strategy for an Insurer with Exogenous Liability

LI Chanjuan1, LI Zhongfei2,3, ZENG Yan2   

  1. (1. School of Mathematics and Computational Science, Sun Yatsen University, Guangzhou 510275, China;〖JP〗2. Lingnan (University) School, Research Center for Financial Engineering and Risk Management, Sun Yatsen University, Guangzhou 510275, China;3.School of Business,Sun Yatsen University, Guangzhou 510275,China)
  • Received:2011-06-29 Revised:1900-01-01 Online:2012-01-25 Published:2012-01-25

摘要: 研究了外生负债影响下保险公司的最优再保险投资策略,其中假设保险公司的目标是最大化终端财富的期望指数效用;盈余过程服从扩散模型;风险资产和负债均由几何布朗运动刻画。运用随机动态规划方法,得到了保险公司在 (i) 进行投资且允许购买比例再保险或获取新业务,(ii) 进行投资但只允许购买比例再保险,不能获取新业务,两种情形下的最优再保险投资策略以及最优值函数的解析式。最后,采用数值算例阐述了外生负债与市场参数对最优策略的影响。

关键词: 投资组合, 再保险, 资产负债管理, 最大化效用, 外生负债

Abstract: The optimal reinsurance-investment strategy for an insurer with an exogenous liability is considered. Assume that the aim of the insurer is to maximize the expected exponential utility of the terminal wealth; the surplus process of the insurer follows a diffusion model while the risky assets' prices and the exogenous liability are governed by geometric Brownian motions. By employing the stochastic dynamic programming, the closed form of the optimal reinsuranceinvestment strategy and the optimal value function are derived under two cases: (i) the insurer can invest in a financial market and purchase proportional reinsurance or acquire new business, (ii) the insurer can invest in a financial market and purchase proportional reinsurance, but not acquire new business. Finally, a numerical example is given to show the impact of the exogenous liability and the market parameters on the optimal strategy.

Key words: portfolio, reinsurance, asset-liability management, utility maximization, exogenous liability

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