基于通货膨胀和最低保障的DC养老金最优投资

Optimal Investment of DC Pension under the Inflation and Minimum Guarantee

主要研究了通货膨胀和最低保障下的DC养老金的最优投资问题。首先,应用伊藤公式得到通胀折现后真实股票价格的微分方程。然后,在DC养老金终端财富外部保障约束下,引入欧式看涨期权,考虑随机通胀环境下的退休时刻终端财富期望效用最大化问题,应用鞅方法推导退休时刻以及退休前任意时刻DC养老金最优投资策略的显式解。最后,应用蒙特卡洛方法对结果进行数值分析,分析最低保障对DC养老金最优投资策略的影响。

This paper mainly studies the optimal investment problem of DC pension under the inflation and minimum guarantee. First, we use the Ito formula to derive the stochastic differential equation for the real stock price discounted by inflation. And then, introducing European call options and considering the problem of maximizing the expected utility of terminal wealth discounted by inflation at retirement under the minimum guarantee, we use the martingale method to derive the explicit solution of the optimal investment strategy of DC pension at retirement and any time before retirement. In the end, we analyze the impact of the minimum guarantee on the optimal investment strategy of DC pension through using the Monte-Carlo method.