退休计划中整合消费、投资和年金的最优决策研究

Optimal Decision-making of Consumption,Investment and Annuity Purchasing in Retirement Plan

在人口老龄化和人口长寿背景下,退休者如何配置其在工作期间积累的总财富,才能规避风险并获得较高收益和最大终身福利,是人们关注的重要问题。本文针对达到退休年龄的人群,考虑其退休后的消费、投资和年金配置问题,首先将利率风险和股票风险引入退休者的生命周期模型,得到更加全面的金融市场模型。然后基于Epstein-Zin效用模型,综合考虑退休者的消费效用和遗产需求,求解随机环境下退休者的消费、债券投资、股票投资和购买年金的决策问题。最后,本文展示了在不同的参数设置下退休者如何通过一系列决策实现期望效用的最大化。结果表明:实现效用最大化要求退休者在退休早期配置大量年金;当金融市场(利率,股票)参数变化时,退休者仍需配置大量的年金来提高效用;购买年金能够显著提高退休者的消费水平;遗产动机的增大会减少购买年金的份额;另外,退休者对未来预期寿命的主观低估会降低年金的购买份额;最后,退休者的跨期替代弹性和风险厌恶水平会对各种选择行为产生重要影响。

In the background of population aging and longevity,how retirees allocate their total wealth accumulated during their work to hedge risks,achieve higher utility and maximize lifetime benefits,is an important issue of concern.This paper considers the optimal allocations of consumption,investment and annuity after retirement for an individual.Firstly,in order to obtain a more comprehensive model of financial market,we introduce the interest rate risk and equity risk in the retirees’ life cycle model.Then based on the Epstein-Zin utility model,the retirees’ consumption and bequest motive are considered comprehensively.Moreover,the optimal allocations of retirees’ consumption,bond investment,stock investment and annuity purchasing in stochastic environment are solved by numerical method.Finally,this paper shows the decision of retirees to maximize the expected utility function with different parameter settings.The results show that:The retirees should purchase a large number of annuities in the early stages of retirement;when parameters of financial market(interest rate,equity) change,retirees still need to allocate a large amount of annuities to maximize utility;annuity can significantly increase the consumption level of retirees;the increase of bequest motive will reduce the purchase of annuities;in addition,subjective underestimation of future life expectancy will reduce the purchase of annuities;finally,the elasticity of intertemporal substitution and the coefficient of relative risk aversion also have a significant impact on the behavior of retirees.