摘要
作为金融市场体系的重要组成部分,选择最优的投资和再保险策略对保险公司来说十分重要.本文研究了保险公司在均值-方差准则下的最优投资和再保险问题,假设保险公司通过购买比例再保险来分散自身风险,其盈余过程由近似经典Cramer-Lundberg模型的扩散过程刻画,此外,保险公司通过投资于无风险资产和风险资产来增加收入,其中风险资产价格服从Volterra Heston模型.由于Volterra Heston模型的非马尔可夫性和非半鞅性,经典的随机最优控制框架不再适用,本文通过构造一个辅助随机过程,得到了依赖于Riccati-Volterra方程解的最优投资和再保险策略及有效前沿,并对最优策略、有效前沿和波动率粗糙度、再保险因素之间的关系进行了数值分析,发现股票价格的波动率越粗糙,保险公司对股票市场和再保险的需求越大.
As an important part of the financial market system,it is very important for insurance companies to choose the optimal investment and reinsurance strategies.This paper considers an optimal reinsurance and investment problem for an insurance firm under the criterion of mean-variance.Assume that insurers diversify their risk by purchasing proportional reinsurance,which the surplus process is a diffusion process similar to the classical Cramér-Lundberg model.In addition,insurers increase their income by investing in risk-free assets and risky assets,which the prices of risky assets follow the Volterra Heston model.Due to the non-Markovian and non-semimingale properties of the Volterra Heston model,the classical stochastic optimal control framework is no longer applicable.By constructing an auxiliary stochastic process,we obtain the optimal investment and reinsurance strategies and the efficient frontier,which depend on the solution to a Riccati-Volterra equation.Finally,we numerically analysis the relationship among optimal strategies,effective frontier,volatility roughness and reinsurance factors.It is found that the rougher the volatility of stocks,the greater the demand of insurance companies for stocks and reinsurance.
作者
候惠敏
周清
HOU HUIMIN;ZHOU QING(School of Science,Beijing University of Posts and Telecommunications,Beijing 100876,China)
出处
《应用数学学报》
CSCD
北大核心
2024年第1期82-100,共19页
Acta Mathematicae Applicatae Sinica
基金
国家自然科学基金(11871010,11971040)
中央高校基本科研业务费专项资金(2019XD-A11)资助项目。
