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应用数学学报  2013, Vol. 36 Issue (5): 791-802    DOI:
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跳-扩散风险模型的最优投资和再保险策略
林祥1, 李艳方2
1. 中南大学数学与统计学院概率统计研究所, 长沙 410075;
2. 河南理工大学数学与信息科学学院, 焦作 454000
Optimal Investment and Optimal Reinsurance Policy for Jump-Diffusion Risk Model
LIN Xiang1, Li Yanfang2
1. School of Mathematics and Statistics, Central South University, Changsha 410075;
2. School of Mathematics, Henan Polytechnic University, Jiaozuo 454000
 全文: PDF (373 KB)   HTML (1 KB)   输出: BibTeX | EndNote (RIS)      背景资料
摘要 本文对跳-扩散风险模型, 在赔付进行比例再保险, 以及盈余投资于无风险资产和风险资产的条件下, 研究使得最终财富的指数期望效用最大的最优投资和比例再保险策略. 得到最优投资策略和最优再保险策略, 以及最大指数期望效用函数的显式表达式, 发现最优策略 和值函数都受到无风险利率的影响. 最后通过数值计算, 得到最优投资和比例再保险策略, 以及值函数与模型各个参数之间的关系.
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林祥
李艳方
关键词投资   比例再保险   HJB方程   指数效用函数     
Abstract: In this paper, we consider an insurance company whose surplus is modeled by a jump diffusion risk process. The insurance company can invest the surplus in a risk-free asset and a risky asset, and purchase proportional reinsurance for claims. Our main goal is to find an optimal investment and proportional reinsurance policy which maximizes the expected exponential utility of terminal wealth. We obtain the close form expressions for the value function, optimal investment and proportional reinsurance policy. We find that the optimal policy and the value function depend on the risk-free rate. We also investigate the effects of the parameter on the optimal investment and proportional reinsurance policy and the value function by numerical calculation, respectively.
Key wordsinvestment   proportional reinsurance   HJB equation   expected exponential utility   
收稿日期: 2009-06-25;
基金资助:国家自然科学基金(11271375;11201125)资助项目.
引用本文:   
林祥,李艳方. 跳-扩散风险模型的最优投资和再保险策略[J]. 应用数学学报, 2013, 36(5): 791-802.
LIN Xiang,Li Yanfang. Optimal Investment and Optimal Reinsurance Policy for Jump-Diffusion Risk Model[J]. Acta Mathematicae Applicatae Sinica, 2013, 36(5): 791-802.
 
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