Cobb-Douglas效用和Epstein-Zin递归效用下个人年金账户的最优投资和给付策略  

Optimal Asset Allocation and Life Annuity Payment Strategy under Cobb-Douglas Utility and Epstein-Zin Recursive Utility

作　　者：王愫新 荣喜民 赵慧 WANG Suxin;RONG Ximin;ZHAO Hui(School of Finance,Tianjin University of Finance and Economics,Tianjin 300222;School of Mathematics,Tianjin University,Tianjin 300072)

机构地区：[1]天津财经大学金融学院,天津300222 [2]天津大学数学学院,天津300072

出　　处：《工程数学学报》2025年第1期139-158,共20页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11901427,12171360,11771329,12371475,11871052);天津市自然科学基金(20JCYBJC01160);天津财经大学青苗计划。

摘　　要：生命年金在养老金的提取阶段发挥了重要作用,它能够帮助人们有效应对长寿风险。考虑了连续时间下个人年金计划的随机模型,参保人的年金账户初始价值是提前确定的,而年金的给付取决于账户的财务状况。年金管理者在无风险资产和风险资产上进行投资以获取收益,调整年金给付水平并收取管理费,以保证该计划的稳定运行。在目标函数中我们考虑年金调整额与管理费加权乘积的效用最大化,并用Cobb-Douglas效用刻画参保人和管理者的风险偏好。通过随机控制理论建立优化问题的Hamilton-Jacobi-Bellman方程,进而得到最优策略和价值函数的解析式。此外,我们将模型拓展到Epstein-Zin递归效用下的最优控制问题,发现了跨期替代弹性对年金给付调整和管理费的正向影响。最后通过数值算例分析了模型参数对最优策略的影响,并给出相应的经济解释,验证了该年金计划能够为参保人提供稳定的、持续的年金给付。Life annuity plays an important role in the withdrawal phase of pensions,and it can help people deal with longevity risks effectively.This paper considers a stochastic model for a life annuity plan in continuous time,where the initial value of the individual annuity account is determined in advance,while the annuity payments depend on the financial situation of the account.The annuity fund is allowed to invest in a risk-free asset and a risky asset.The fund manager can adjust the annuity payment level and charge management fees to ensure the stable operation of the plan.In the objective function,we aim to maximize the utility of the weighted product of the annuity payment adjustment and the management fee,which is taken in the form of Cobb-Douglas utility.By applying dynamic programming approach,we establish the corresponding Hamilton-Jacobi-Bellman equation and derive the optimal strategies and the value function explicitly.Furthermore,the Epstein-Zin recursive utility is considered as an extension and we find the elasticity of intertemporal substitution has a positive effect on the annuity payment adjustment and the management fee.Numerical examples are presented to illustrate the sensitivity of the optimal strategies to model parameters,and the corresponding economic explanations are given,which demonstrate that this annuity plan is sustainable and can provide stable annuity payment for participants.

关 键 词：生命年金 Cobb-Douglas效用 Epstein-Zin递归效用 动态规划 最优投资 

分 类 号：F830[经济管理—金融学]