首次在均值-方差效用下研究了带有死亡风险的退休后最优投资和年金化比例决策. 假设在退休时刻, 退休者按一定的比例将累积财富购买一个即期终身年金, 之后终身获得一个年金收入, 并将消费后的财富进行相应的投资决策, 直到死亡时刻为止, 以最优化遗产效用的均值-方差效用. 利用拉格朗日乘子法、动态规划方法和数值分析方法, 分两步骤得到了最优的投资和年金化比例策略. 利用数值分析技术, 分析了遗产动机、退休者预期寿命以及退休年龄对最优投资金额、年金化比例和最优值函数的影响, 部分结果验证了年金产品能降低退休者的投资风险. 本文的理论结果表明, 退休后风险管理常用的目标定位模型所得结果是均值-方差模型所得结果的特殊情形;数值分析结果表明, 与传统的目标定位模型相比, 均值-方差模型在大部分情况下能降低遗产水平低于预设目标值的发生概率, 同时能大幅度提高遗产水平远超预设目标值的概率.
Abstract
This paper first adopts the mean-variance criterion to study the optimal portfolio selection and annuitization proportion post-retirement with mortality risk. Assume that at retirement, the retiree spends a proportion of her accumulated wealth on a lifetime immediate annuity. Then the retiree will receive a lifetime income and invests her wealth after consumption in the available assets until death in order to optimize the mean-variance utility of her bequest. By Lagrange multiplier technique, dynamic programming and numerical analysis, we obtain the optimal investment strategy and annuitization proportion in two steps. Furthermore, numerical examples are provided to analyze the effects of the bequest motivate, the expected lifespan and the retirement age on the optimal investment strategy, annuitization proportion and the optimal value function. Some results show that the annuity product can reduce the investment risk of the retirees. The mathematical results in this paper show that the obtained results in the target-based model commonly used in the post-retirement risk management are special cases of those in the mean-variance model; the numerical results indicate that in most cases, the mean-variance model can reduce the probability that the bequest level is lower than the pre-determined target value meanwhile can greatly increase the probability that the bequest level is far beyond the target value.
关键词
领取阶段 /
最优投资金额 /
最优年金化比例 /
均值-方差模型 /
动态规划方法
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Key words
decumulation phase /
optimal investment amount /
optimal annuitization proportion /
mean-variance model /
dynamic programming
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脚注
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基金
国家自然科学基金(11671411);中央高校基本科研业务费专项资金;中央财经大学科研创新团队支持计划项目;教育部人文社会科学重点研究基地重大项目(22JJD790091);保险风险分析与决策学科创新引智基地(B17050)
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