CEV模型下考虑风险相关性的保险组合时间一致性投资策略

Time-Consistent Investment Policy for Insurance Portfolio with Dependent Risk in the CEV Model

在均值方差准则下研究了保险组合的时间一致投资策略。假定风险资产价格服从不变弹性方差(CEV)模型,保险盈余过程为扩散近似模型。考虑到金融市场和保险市场的不完全风险相关性,假设驱动CEV模型的布朗运动和驱动盈余过程的布朗运动存在部分相关。通过求解问题对应的扩展哈密顿-雅克比-贝尔曼(HJB)方程组,得到了值函数和最优时间一致投资策略的显式解。结果表明,考虑风险相关性后均值方差保险组合选择问题等价于一个普通组合选择问题加上一个保险组合的最优时间一致对冲问题;忽视风险相关性将对风险厌恶型投资者的福利造成显著的损失。

Thispaper investigatesthe time-consistent investmentpolicy for insuranceportfoliowiththe mean-variance criterion.The price process of the risky asset follows the constant elasticity of variance(CEV)model,and the surplus process is described by a diffusion approximation model.Moreover,considering the imperfect risk correlation between the financial market and the insurance sector,it is assumed that the Brownian motion driving CEV model is imperfectly correlated with the Brownian motion driving earnings process.By solving the associated extended Hamilton-Jacobi-Bellman(HJB)equations,the value functions and the optimal time-consistent investment policy in explicit form are obtained.It is found that the mean-variance insurance portfolio choice problem is equivalent to a mean-variance common portfolio choice problem and an optimal time-consistent hedging problem for insurance portfolio after introducing the risk dependence.The risk-averse investor will suffer significant economic cost it ignoring the risk dependence.