基于Legendre变换的最优再保险投资策略  

Optimal reinsurance-investment strategy with Legendre transform

作　　者：陈子旸 王秀莲[1] CHEN Zi-yang;WANG Xiu-lian(College of Mathematical Science,Tianjin Normal University,Tianjin 300387,China)

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《陕西理工大学学报（自然科学版）》2022年第4期61-68,共8页Journal of Shaanxi University of Technology:Natural Science Edition

基　　金：国家自然科学基金项目(11401436);天津市教育委员会科研基金项目(JW1714)。

摘　　要：针对保险公司终端财富最大化的最优再保险投资策略问题,分别考虑了费率定价过程服从相关索赔保费原则和无相关索赔保费原则两种情况。对目标函数的初始问题通过Legendre变换转化为对偶问题,在对数效用函数目标下,得到最优再保险投资策略的解析式。通过实例分析展现了相关参数对最优策略的影响。With regard to the optimal reinsurance and investment strategy under the principle of correlated claims premium,the study considers the case when the rate pricing process obeys the correlated claims premium principle and the uncorrelated claim premium principle.The primary problem of the objective function is transformed into the dual problem by Legendre transform.Under the objective of logarithmic utility function,the closed-form solutions for optimal reinsurance-investment strategy are obtained.The example is given to analyze the effects of parameters on the optimal reinsurance and investment strategy.

关 键 词：LEGENDRE变换 比例再保险 相关索赔保费原则 最优投资 对数效用函数 

分 类 号：O211.67[理学—概率论与数理统计]