带遗产动机和最低业绩约束的DC型养老金的优化投资问题

Optimal Investment Strategy of DC Pension Plan with Bequest Motivation and Minimum Performance Constraints

研究了DC型养老金计划模式下的资产配置问题,涉及养老金计划参与者的遗产动机、退休前的工资流、退休后的最低生活保障和基金管理者的最低业绩需求,既考虑了养老金计划参与者的利益,又兼顾了基金管理者对业绩的基本要求.建模时,假设养老基金可投资于无风险资产、指数债券和股票.基金管理者的目标是最大化终端盈余(即养老金账户的终端财富超过养老金计划参与者的最低生活保障的部分)的期望效用.应用Lagrange方法,得到了最优终端盈余,进而得到了最优终端财富;同时利用鞅方法,得到了最优投资策略和财富过程.在此基础上,给出了数值算例,考察了一些重要参数对最优投资策略的影响.结果发现遗产水平、最低业绩水平、贡献初值、最低生活保障初值和财富初值都会影响基金管理者对经济环境状态的判断,进而影响其投资行为.

This paper studies an asset allocation problem under the DC pension plan,involving the bequest motivation,the wage flow before retirement and minimum living guarantee after retirement of a pension plan member,and the minimum performance demand of the fund manager.This setting considers not only the benefits of the pension plan member,but also the basic performance requirement of the fund manager.The pension fund can be invested in one risk-free asset,an index bond and a stock.The goal of the fund manager is to maximize the expected utility of the terminal surplus,which is the part of the terminal wealth that exceeds the minimum living guarantee.Using the Lagrange method,we obtain the optimal terminal surplus,and then obtain the optimal terminal wealth.Meanwhile,we provide the optimal investment strategies and wealth process by the martingale approach.Finally,numerical examples are given to examine the influence of some important parameters on investment strategies.The results show that the bequest level,the minimum performance level,the initial contribution,the initial minimum living guarantee and the initial wealth all affect the fund manager’s judgment for economic environment states,thus further affecting her/his investment behaviors.