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主观死亡评估下的退休后投资-消费-年金化时刻决策

Optimal investment,consumption and annuitization time for post-retirement decision with subjective mortality probabilities

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考虑退休者的死亡风险和遗产效用,研究了退休后期最优投资-消费-年金化时刻决策问题.根据退休者在退休时刻对自身死亡概率的主观评估,把退休者分为两大类:第一类退休者自我评估以概率1 活不到最大年金化时刻,第二类退休者自我评估以一定概率活得过最大年金化时刻.自退休时刻开始到死亡时刻或年金化时刻为止,退休者要进行投资和消费决策.假设最优的年金化时刻是使得年金化前后的累计消费效用均值以及遗产效用均值之和达到最大.采取幂效用函数形式,得到了最优投资-消费策略的解析解、第一类退休者在生存期内都不购买年金的条件以及第二类退休者选择在最大年金化时刻购买年金的条件.利用数值分析方法,详细分析了性别、生存周期、遗产效用、折现函数、风险厌恶系数、金融投资环境以及年金产品价格对退休者年金行为的影响.
This paper studies the optimal post-retirement investment,consumption,and annuitization time for the retirees with mortality risk and bequest utility.According to the subjective mortality probability at retire-ment,the retirees are divided into two groups:the first group cannot live up to the maximum annuitization time with a probability of one,and the second group can live up to the maximum annuitization time with a certain probability less than one.Since retirement,the retirees need to determine the investment and consumption un-til the death time or the annuitization time.The optimal annuitization time is the time that maximizes the sum of the cumulated expected consumption utilities before and after purchasing an annuity and the expected be-quest utility.By adopting a power utility function,this paper obtains the closed-form optimal investment-con-sumption strategy and the conditions under which the first group of the retirees do not buy the annuity through-out the lifetime and the second group buy the annuity at the maximum annuitization time.Finally,a numerical analysis is provided to analyzethe effects of gender,the survival period,the bequest utility,the discount func-tion,the risk aversion,the financial environment,and the annuity price on the annuitization behaviors of the retirees.

post-retirementoptimal investment,consumption and annuitization timemortality riskbequest utilitydynamic programming

伍慧玲、廖朴

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中央财经大学中国精算研究院,北京 102206

退休后期 最优投资-消费-年金化时刻决策 死亡风险 遗产效用 动态规划

国家自然科学基金资助项目中央高校基本科研业务费专项教育部人文社会科学重点研究基地重大项目保险风险分析与决策学科创新引智基地项目

1167141122JJD790091B17050

2024

10.19920/j.cnki.jmsc.2024.03.005

管理科学学报
天津大学 国家自然科学基金委员会管理科学部

管理科学学报

CSTPCDCSSCICHSSCD北大核心
影响因子：2.573
ISSN：1007-9807
年,卷(期)：2024.27(3)
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