随机通货膨胀下DB养老金计划最优退出策略

针对目前投保人在投保过程遇到的系统性风险,研究了基于随机通货膨胀风险下DB养老金计划的最优退出策略问题。该计划具有最低保障功能,并且投保人可以在任何时期行使surrender期权。为了找到行使surrender期权的最佳时间,将带有surrender期权的DB型年金计划的最佳退出时间转化为一个自由边界问题,由此可以得到一个相应的非齐次偏微分方程,利用梅林变换对非齐次偏微分方程进行积分变换后使用RIM递推积分法对积分方程进行数值求解,从而得到一个surrender期权估值的积分方程和最优退出边界。研究表明:这种期权为投保人提供了更多的保护,使得投保人拥有更多的选择权;此外,用数值分析给出了公平收费率的性质和在不同投资比例对账户价值的影响以及其最优退出策略。

Optimal Surrender Strategy of DB Pension Plan under Random Inflation

In view of the systemic risks encountered by policy holders in the insurance process, the optimal surrender strategy of DB pension plan based on random inflation risk is studied. The scheme has a minimum protection function, and policy holders can exercise surrender options at any time. In order to find the best time to exercise surrender option, the optimal exit time of DB annuity plan with surrender option can be transformed into a free boundary problem. From this, a corresponding nonhomogeneous partial differential equation can be obtained. After the integral transformation of the nonhomogeneous partial differential equation is carried out by using Merlin transformation, the integral equation is solved by RIM recurrence integration method, and an integral equation and the optimal exit boundary of surrender option estimation are obtained. The research shows that this option provides more protection for the policy holder and makes the policy holder have more options. In addition, we use numerical analysis to give the nature of fair rate and the influence of different investment ratios on account value, as well as its optimal surrender strategy.