VaR约束下最优比例再保险和投资策略问题

Optimal Ratio Reinsurance and Investment Strategy under VaR Constraint

研究了VaR动态约束下保险人的最优投资和再保险策略选择问题.假设保险人选择比例再保险来分散索赔风险,并通过银行存款和投资股票的手段来增加额外收益,其中股票价格满足Heston模型.保险人的目标是寻求使其终端财富的期望效用最大的最优策略.引入VaR约束条件并采用期望效用最大化为准则,运用随机控制理论建立具有VaR约束的随机控制问题,采用动态规划推导HJB方程,并利用Lagrange函数等方法得到指数效用下VaR约束有效和无效时的最优策略.另外,考虑了仅投资情形下的最优投资策略.最后通过仿真对最优策略进行敏感性分析.

This paper investigates the optimal investment and reinsurance strategy selection problem for an insurer under VaR dynamic constraints.Suppose that the insurer chooses proportional reinsurance to spread the claims risk and increase the extra return by means of bank deposit and stock investment,where the stock price satisfies the Heston model.The goal of the insurer is to seek the optimal strategy that maximizes the expected utility of its terminal wealth.By introducing the VaR constraint condition and using the expected Utility maximization criterion,the stochastic control problem with VaR constraint is established,and then the HJB equation is derived by using the stochastic control theory.Furthermore,by using Lagrange functions and other methods,the optimal strategies under exponential utility are obtained when the VAR constraints are active and inactive for the insurer.In addition,the optimal investment strategy for the only investment case is considered.Finally,the sensitivity of the optimal strategy is analyzed by simulation.