部分信息和损失厌恶下的最优投资与再保险  

Optimal investment and reinsurance under partial information and loss aversion

作　　者：陈凤娥[1] 季锟鹏 彭幸春 CHEN Feng’e;JI Kunpeng;PENG Xingchun(School of Science,Wuhan University of Technology,Wuhan 430070,China)

机构地区：[1]武汉理工大学理学院,武汉430070

出　　处：《系统工程理论与实践》2024年第3期932-946,共15页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(11701436);教育部人文社会科学基金(22YJAZH087);中央高校科研业务费专项资金(3120621545)。

摘　　要：该文研究了具有损失厌恶特征的保险公司在仅拥有部分信息时的最优投资与再保险策略.首先,利用滤波技术将问题进行转化.然后,在期望S型效用最大化准则下,运用鞅方法,偏微分方程,傅里叶变换和逆变换方法得到了最优投资与再保险策略的半解析表达式.最后,利用蒙特卡罗方法进行数值分析.结果表明忽略学习下的最优投资与再保险比例比滤波估计下的更低,而且在参考点水平较高时,相比较最优再保险与通胀指数债券投资比例,忽略学习对最优股票投资比例的影响更显著.另一方面,幂效用下的最优策略比S型效用下的最优策略更加激进,其中最优再保险比例在两种效用函数情形差别最大,这说明心理因素对再保险策略的影响最显著.This paper studies the optimal investment and reinsurance strategy for an lossaversed insurer under partial information.First,the filtering technique is used to transform the problem.Then,under the expected S-shaped utility maximization criterion,the semi-analytical expression of optimal investment and reinsurance strategy is derived by using martingale method,partial differential equation,Fourier transform and inverse transform method.Finally,the Monte Carlo method is used in the numerical analysis.The results show that the optimal ratios of investment and reinsurance under ignoring learning are lower than that under filtering estimation.When the reference point level is higher,compared with the ratios of optimal reinsurance and investment in inflation index bond,ignoring learning has a greater effect on the optimal ratio of investment in stock.On the other hand,the optimal strategy under the power utility is more aggressive than the optimal strategy under the S-shaped utility,and the optimal reinsurance ratio has the largest difference under the two types of utility functions,which shows that psychological factors have the most significant impact on the reinsurance strategies.

关 键 词：S型效用 部分信息 投资 再保险 

分 类 号：O225[理学—运筹学与控制论] O211[理学—数学] F840[经济管理—保险]