指数保费准则下的最优投资和比例再保险

数学物理学报 ›› 2014, Vol. 34 ›› Issue (5): 1161-1172.

指数保费准则下的最优投资和比例再保险

陈密¹, 郭军义²

1.福建师范大学数学与计算机科学学院福州 350108;
2.南开大学数学科学学院天津 300071

收稿日期:2012-05-04 修回日期:2013-10-05 出版日期:2014-10-25 发布日期:2014-10-25
基金资助:
国家自然科学基金(11171164, 11371020)资助

Optimal Investment and Proportional Reinsurance under Exponential Premium Calculation

CHEN Mi¹, GUO Jun-Yi²

1.School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350108;
2.School of Mathematical Sciences, Nankai University, Tianjin 300071

Received:2012-05-04 Revised:2013-10-05 Online:2014-10-25 Published:2014-10-25
Supported by:
国家自然科学基金(11171164, 11371020)资助

摘要/Abstract

摘要：

该文研究了保险公司的最优投资和比例再保险问题, 其中假定保险公司的盈余过程为一个带扩散扰动的经典风险过程. 假定再保险的保费按照指数保费原理来计算, 这使得所研究的随机控制问题成为非线性的. 该文同时考虑了最大化终端财富指数效用和最大化调节系数两类问题, 并给出了最优值函数和相应的最优策略的解析表达. 此外, 该文还分析了再保险公司的风险厌恶和保险公司的不确定性参数对最优策略的影响.

关键词: 投资, 比例再保险, 指数保费原理, 调节系数, 指数效用

Abstract:

This paper studies the optimal investment and proportional reinsurance policies of an insurer whose insurance business follows a diffusion perturbed classical risk process. It is assumed that the reinsurance premium is calculated according to the exponential premium principle which makes the stochastic control problems to be nonlinear. The problems of maximizing the adjustment coefficient and the expected exponential utility of terminal wealth are considered.
In both of the problems, explicit expressions for their optimal value functions and the corresponding optimal strategies are obtained. Furthermore, the influences of the risk aversion of the reinsurance company and the uncertainty of the insurance company on the optimal strategies are analyzed.

Key words: Investment, Proportional reinsurance, Exponential premium principle, Adjustment coefficient, Exponential utility

中图分类号:

60J75

陈密, 郭军义. 指数保费准则下的最优投资和比例再保险[J]. 数学物理学报, 2014, 34(5): 1161-1172.

CHEN Mi, GUO Jun-Yi. Optimal Investment and Proportional Reinsurance under Exponential Premium Calculation[J]. Acta mathematica scientia,Series A, 2014, 34(5): 1161-1172.

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