基于Cobb-Douglas及递归效用函数的养老金最优资产配置策略研究

刘伟; 丁逸康; 赵睿杰; 杜俐; 马玉梅

doi:10.13568/j.cnki.651094.651316.2024.01.09.0002

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基于Cobb-Douglas及递归效用函数的养老金最优资产配置策略研究

数理科学 | 更新时间：2026-01-21

- 基于Cobb-Douglas及递归效用函数的养老金最优资产配置策略研究
- 基于Cobb-Douglas及递归效用函数的养老金最优资产配置策略研究
- 新疆大学学报（自然科学版中英文） 2025年42卷第1期页码：24-35
- 作者机构：
  
  新疆大学数学与系统科学学院
- 作者简介：
- 基金信息：
  
  国家自然科学基金“金融保险中的多维风险度量与最优控制问题研究”（11961064）;新疆维吾尔自治区大学生创新项目“基于Cobb-Douglas效用函数的养老金最优资产配置策略研究”（S202210755095）
- DOI：10.13568/j.cnki.651094.651316.2024.01.09.0002
  中图分类号： F842.67;F224
- 纸质出版：2025
- 稿件说明：
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[1]刘伟,丁逸康,赵睿杰,等.基于Cobb-Douglas及递归效用函数的养老金最优资产配置策略研究[J].新疆大学学报(自然科学版中英文),2025,42(01):24-35+47.
[1]刘伟,丁逸康,赵睿杰,等.基于Cobb-Douglas及递归效用函数的养老金最优资产配置策略研究[J].新疆大学学报(自然科学版中英文),2025,42(01):24-35+47. DOI： 10.13568/j.cnki.651094.651316.2024.01.09.0002.

DOI：10.13568/j.cnki.651094.651316.2024.01.09.0002.

摘要

研究考虑长寿趋势的目标收益型养老金的最优投资和收益调整问题.采用改进的死亡力模型

将养老金计划参与者的长寿趋势引入养老金的决策管理问题中.以期望效用最大为优化准则

建立随机控制模型

其中效用函数分别采用Cobb-Douglas效用函数以及递归效用函数.针对金融市场模型不确定的特点

采用鲁棒方法求解最优控制策略.运用动态规划方法

通过求解相应HJB (Hamilton-Jacobi-Bellman)方程

得到值函数和控制策略的显式表达式.最后通过数值分析

给出两类效用下重要参数对最优控制策略的影响.

Abstract

This paper investigates the optimal investment and benefit adjustment for target benefit pension plan considering the longevity trend. By using the Cobb-Douglas utility function and maximizing expected utility as the optimization criterion

we aim to find robust control strategies that account for the uncertainty in the financial market models. Based on stochastic control theory

the Hamilton-Jacobi-Bellman(HJB) equation is solved to obtain explicit solutions for the value function and control strategies. Finally

numerical analysis is conducted to study the impact of influencing factors on the strategies.

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Keywords

references

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