保险与再保险及市场对冲稳健均衡策略

Robust Equilibrium Strategies for Insurance and Reinsurance with Market Hedging

假设保险公司的资本盈余过程服从复合Poisson风险跳过程,保险公司通过向再保险公司购买比例再保险来分散保险风险,保险公司和再保险公司均基于方差原则收取保险费率.两个公司都可以投资于金融市场,其中风险资产的价格过程服从几何布朗运动.假设保险公司和再保险公司都是模糊厌恶的且具有指数效用函数,基于保险公司与再保险公司加权终期财富效用最大化目标,利用动态规划原理,得到了两公司的稳健均衡比例再保险和投资组合策略的解析表达式.分析了均衡条件下的风险投资,再保险价格与保险公司自保险比例受不同参变量影响的变化特征.

This paper assumes that the capital surplus process of insurance companies follows a compound Poisson risk jump process.Insurance companies distribute insurance risks by purchasing proportional reinsurance from reinsurance companies,and all the companies charge premium rates based on the principle of variance.Both the companies can invest in financial markets,where the price process of the risky assets follows a Geometric Brownian motion.Under the assumption that insurance companies and reinsurance companies are both ambiguity-averse and have exponential utility functions,the objectives of insurer and reinsurer are to maximize the utility of their weighted terminal wealth.By using the principle of dynamic programming,the analytic expressions of the two types of companies' robust equilibrium proportional reinsurance and portfolio strategy are obtained.Finally,the changing characteristics of the risk investment,the reinsurance price and the self-insurance ratios of the insurance company affected by different parameter variables under the equilibrium condition are analyzed.