Heston模型下基于HARA效用的最优投资-再保险策略研究  

Study on Optimal Reinsurance and Investment Strategy with HARA Utility Under Heston Model

作　　者：张燕 周华任 倪艳 ZHANG Yan;ZHOU Hua-ren;NI Yan(Department of General Education,Army Engineering University of PLA,Nanjing 211101,China)

机构地区：[1]陆军工程大学基础部,江苏南京211101

出　　处：《数学的实践与认识》2025年第2期59-72,共14页Mathematics in Practice and Theory

基　　金：陆军工程大学基础前沿科技创新项目。

摘　　要：主要研究双曲绝对风险(HARA)期望效用最大化下的最优投资-再保险策略问题.为避免风险,允许保险人购买比例再保险,且可以投资一种无风险资产和一种价格服从Heston模型的风险资产.由于HARA效用的复杂结构,导致原问题的HJB方程,尤其是相关系数满足-1<p<1时的HJB方程难以求解,因此本文提出基于勒让德对偶变换和随机控制理论,通过构造对偶HJB方程解的形式来求解原问题的HJB方程,给出了-1≤p≤1对应的HJB方程的求解方法,并得到了最优再保险策略和最优投资策略的解析式.最后通过数值计算,分析了部分参数对最优策略的影响.This paper investigates an optimal reinsurance-investment problem under the criterion of maximizing the expected HARA utility of the insurer's terminal wealth.The insurer is allowed to purchase reinsurance from the reinsurer and is assumed to invest in one risk-free asset and one risky asset whose price follows the Heston model.Due to the complexity of the structure of the solution to the original Hamilton-Jacobi-Bellman(HJB)equation especially for-1<p<1,we use Legendre transform along with the stochastic control theory to change the original non-linear HJB equation into its linear dual one,we provide a method of solving the original HJB equation and we obtain the closed-form solutions of optimal investment-reinsurance strategies for-1≤p≤1,which extends the existing results.Finally,we give some numerical examples to illustrate the impacts of our model parameters on the optimal reinsurance-investment strategy.

关 键 词：HARA效用 再保险 Heston模型 勒让德变换 

分 类 号：G63[文化科学—教育学]