Heston模型下带随机工资的均值-方差DC型养老金计划  

Mean-variance model for defined contribution pension plan with stochastic salary under Heston model

作　　者：李佳奥 常浩[1] 孙秀秀 LI Jia-ao;CHANG Hao;SUN Xiu-xiu(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：《哈尔滨商业大学学报（自然科学版）》2021年第1期87-96,101,共11页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：教育部人文社会科学研究基金规划项目(No.16YJA790004);国家自然科学基金项目(No.71671122,71840005),天津市高校“中青年骨干创新人才培养计划”资助项目.

摘　　要：工资水平决定着养老金缴费水平,而股票价格的波动率是投资决策的重要影响因素.从实际来看,工资水平和股票价格的波动率往往都是随机变化的.为了更加接近实际环境,假设工资水平和股票价格都由Heston随机波动率模型所驱动,建立了一类确定缴费型养老金计划的均值-方差模型.运用随机动态规划原理和拉格朗日对偶原理得到了有效策略和有效边界的显式解,并给出数值算例分析了工资因素和波动率因素对有效策略和有效边界的影响.研究结果表明:随机工资和随机波动率环境下的资本市场线在均值-标准差平面上仍是一条直线;有效策略仅依赖于瞬时工资水平,而有效边界不依赖于工资水平和波动率水平.The level of salary determined the level of pension contribution,and the volatility of stock price was an important factor affecting investment decisions.In practice,the volatilities of salary level and stock price tended to be stochastic.In order to get closer to the actual environment,this paper assumed that both salary level and stock price were driven by the Heston’s stochastic volatility model,and established a mean-variance model for a defined contribution(DC)pension plan.By using the principle of stochastic dynamic programming and Lagrangian duality theorem,obtained the explicit solutions for the efficient strategy and the efficient frontier.A numerical example showed the influence of salary factors and volatility factors on the effective strategy and the efficient frontier.The results showed that the capital market line under the stochastic salary and stochastic volatility was still a straight line in a mean-standard deviation plane.In addition,the effective strategy only depended on instantaneous salary level,while the efficient frontier did not depend on instantaneous salary level and volatility level.

关 键 词：Heston随机波动率模型 随机工资 确定缴费型养老金计划 均值-方差模型 有效策略 有效边界 

分 类 号：O211.67[理学—概率论与数理统计]