变利率下基于SV模型的最优再保险-投资研究  

Optimal Reinsurance and Investment Based on SV Model under Variable Interest Rate

作　　者：夏登峰[1] 苑伟杰 费为银[1] XIA Dengfeng;YUAN Weijie;FEI Weiyin(Department of Financial Engineering,Anhui Polytechnic University,Wuhu 241000,China;School of Statistics and Mathematics,Zhejiang Gongshang University,Hangzhou 310018,China)

机构地区：[1]安徽工程大学金融工程系,安徽芜湖241000 [2]浙江工商大学统计与数学学院,浙江杭州310018

出　　处：《运筹与管理》2023年第6期199-204,共6页Operations Research and Management Science

基　　金：国家自然科学基金资助项目(62273003);安徽省高校自然科学研究项目重点项目(KJ2021A0514)。

摘　　要：对于模糊厌恶型保险商(ambiguity-averse insurer,简称AAI),考虑比例再保险,并将盈余资金在无风险资产和风险资产中进行配置,假设无风险利率是以确定性利率函数表示,而风险资产价格服从Heston随机波动率模型。首先,在模型不确定下,利用Girsanov变换得到保险商的等价财富方程。其次,通过动态规划原理建立了相应的HJB (Hamilton-Jacob-Bellman)方程,并针对CARA (Constant Absolute Risk Aversion)效用函数求解HJB方程,得出最优的再保险-投资策略,最后给出数值模拟并做出经济学解释。The insurance company is an enterprise operating and managing risks.In order to avoid huge losses or even bankruptcy caused by excessive risks in the future operation of insurance companies,on the one hand,insurance companies will use reinsurance to share its risks.On the other hand,insurance companies will make reasonable and effective investment strategies to increase the stability of their own operations.For the past decades,many experts and scholars have studied the optimal reinsurance and investment problems for insurance companies.In general,the optimal reinsurance-investment strategies of insurance companies are considered under three kinds of objective functions.The first kind aims to minimize the ruin probability of insurance company.The second is to maximize the expected exponential utility of terminal wealth of the insurance company.The third type is the mean-variance criterion.For the past years,many scholars have found that stochastic volatility is an important feature of stock price models,as it can better explain the volatility smile,the thick-tailed nature of return distribution,and other features of stock prices.In general,some papers consider the optimal reinsurance and investment strategies of an insurer,where the prices of risk assets are described by GBM(Geometric Brownian Motion) model,O-U(Ornstein-Uhlenbeck process) model and CEV(Constant Elasticity of Variance) model.Compared with the Heston's SV(Heston's Stochastic Volatility) model,none of these models contain full-fledged stochastic volatility assumptions.Moreover,on the one hand,insurance companies have uncertainty in their risk selection preferences when making optimal portfolios.On the other hand,it is difficult to accurately estimate the rate of return of risky assets and the expected surpluses in portfolio management.Therefore,relative to the Ambiguity-Neutral Insurer(ANI),Ambiguity-Averse Insurer(AAI) will look for a way to deal with this uncertainty by considering some alternative models close to the estimated model to arrive at

关 键 词：Heston’s SV模型 确定性利率函数 动态规划原理 稳键的再保险-投资 模糊不确定 

分 类 号：F830.9[经济管理—金融学] O211.63[理学—概率论与数理统计]