均值–方差准则下考虑多种风险的DC型养老金计划  

A Defined Contribution Pension Plan with Multiple Risks under the Mean-Variance Criterion

作　　者：赵磊磊 常浩[1] 李佳奥 ZHAO Leilei;CHANG Hao;LI Jiaao(School of Mathematical Sciences,Tianjin Polytechnic University,Tianjin,300387,China)

机构地区：[1]天津工业大学数学科学学院,天津300387

出　　处：《应用概率统计》2022年第6期847-866,共20页Chinese Journal of Applied Probability and Statistics

基　　金：国家社会科学基金后期资助项目(批准号:21FJYB042)资助。

摘　　要：均值–方差准则下考虑了包含利率风险、波动风险和工资风险在内的一类缴费确定(DC)型养老金最优投资策略问题.在养老金累积阶段,利率水平、波动率水平和工资水平被认为是随机的,且假设利率期限结构满足随机仿射利率模型,股票价格波动率满足Heston随机波动率模型.运用随机动态规划原理以及拉格朗日对偶原理得到了有效策略和有效前沿的显式解.通过数值算例分析了利率因素、波动率因素和工资因素对有效策略和有效前沿的影响.结果表明:随机利率、随机波动率和随机工资环境下的资本市场线在均值–标准差平面上仍是一条直线,且有效策略依赖于瞬时利率水平和瞬时工资水平,而有效前沿不依赖于利率水平、波动率水平和工资水平.This paper studies the optimal investment strategy for a defined contribution pension plan with multiple risks under the mean-variance criterion.In the pension accumulation stage,the level of interest rate,volatility level and wage level are considered to be random,in addition,it is assumed that the term structure of interest rate is driven by the stochastic affine interest rate model,and the stock price is modeled by Heston’s stochastic volatility model.By using the principle of stochastic dynamic programming and Lagrangian duality theorem we obtain the explicit solutions for the efficient strategy and the efficient frontier.A numerical example is given to analyze the effects of interest rate parameters,volatility parameters,and salary parameters on efficient strategies and efficient frontiers.Research results show that the capital market line with interest rate risk,volatility risk and salary risk environments is still a straight line in a mean-standard deviation plane.That is to say,the efficient strategy only depends on both instantaneous interest rate level and instantaneous salary level,while the efficient frontier does not depend on the interest rate level,volatility level and salary level.

关 键 词：仿射利率模型 Heston模型 随机工资 DC型养老金计划 均值–方差模型 

分 类 号：O211.67[理学—概率论与数理统计] F830.48[理学—数学]