带有通胀风险的退休后期最优投资管理

考虑通货膨胀的影响,研究了一个确定缴费养老计划退休后期最优投资决策问题.自退休时刻开始,退休者定期从账户里抽取一定的金额维持日常支出,然后将剩余的财富投资于一个无风险资产、一个股票指数和一个通胀指数债券,直到强制购买年金的时刻.为保障退休后的正常生活,退休者在每个时刻设定投资的目标值,采取二次效用函数衡量投资财富水平和目标值的差距,并选择最优的投资策略以最小化平均累计差距.运用动态规划和随机控制方法,得到了没有上方惩罚的目标值、最优投资策略、最优值函数、破产概率以及终端财富与目标值差距的分布函数等指标的显式表达式.运用数学分析和数值分析手段,得到了每个时刻目标值的性质,分析了终端目标值和消费金额对破产概率的影响,研究了物价指数的瞬间变化率和波动率对财富值与目标值的差距、各时刻财富均值以及破产概率的影响.

Optimal investment strategies post retirement with inflation risk

This paper studies an optimal portfolio selection problem in a defined contribution pension plan during the decumulation phase. The pensioner withdraws an amount for daily-life consumption from the pension fund periodically, and then invests the remaining wealth in a risk-free asset, a stock and an inflation-index bond available in the financial market until the time of compulsory annuitization. The pensioner aims to find the optimal investment strategy to minimize the accumulative expected deviations of the running wealth from the targets, which are measured by the quadratic loss functions. The closed-form expressions for the targets without the penalty of surplus, the optimal investment strategy, the optimal value function, the bankruptcy probability and the distribution of the distance between the terminal wealth and the target are obtained by using the methods of dynamic programming and stochastic control. Finally, mathematical analysis and numerical simulation are presented to study the property of the target at each time, to investigate the effects of the terminal target and withdrawn amount on the bankruptcy probability and to illustrate the effects of the appreciation rate and volatility rate of the inflation on the deviation of the running wealth from the target, the expected wealth at each time and the bankruptcy probability.