跳扩散模型下带违约风险的DC型养老金最优投资策略  

Optimal Investment Strategy for DC Pension Plan with Default Risk under J ump-Diffusion Model

作　　者：李娜 刘伟[1] LI Na;LIU Wei(College of Mathematics and System Science,Xinjiang University,Urumqi,830046,China)

机构地区：[1]新疆大学数学与系统科学学院,乌鲁木齐830046

出　　处：《应用概率统计》2024年第5期725-740,共16页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(批准号:11961064)资助。

摘　　要：本文在跳扩散模型下研究DC型养老金个人账户的最优投资问题.假设养老金管理者将资金投资于一个无风险资产,一支股票及一个可违约债券,其中工资过程与股票的价格过程服从跳扩散模型.由于养老金占参保人退休当期工资的比例(工资替代率)是评价养老金管理绩效的重要标准,因此本文以实现预期工资替代率的精算现值为优化目标建立最优控制模型.运用动态规划方法,通过求解相应的HJB(Hamilton-Jacobi-Bellman)方程得到违约前和违约后的最优投资策略与值函数的显式表达式.最后,通过数值分析表明:股票价格过程与参保人工资过程中的跳跃对最优投资策略有很大影响.当参保人的工资上涨可能性较大时,管理者需加大对股票和可违约债券的投资;当股票价格上涨可能性较大时,管理者会加大对股票的投资.This paper investigates the optimal investment problem of DC pension personal accounts under jump diffusion model.Suppose a pension manager invests in a risk-free asset,a stock and a defaultable bond,where the wage process and the stock price process obey the jump-diffusion model.Since wage replacement rate is an important standard to evaluate pension management performance,this paper establishes an optimal control model with actuarial present value of wage replacement rate as the optimization goal.An explicit expression for optimal investment strategy and value function is obtained by solving the corresponding Hamilton-Jacobi-Bellman equation using dynamic programming method.Finally,the numerical analysis shows that the jump in the process of stock price and the insured’s salary have a significant impact on the optimal investment strategy.When the salary of the insured is likely to rise,the managers will increase the investment in stocks and defaultable bonds.When stock prices are likely to rise,the managers will increase their investment in stocks.

关 键 词：DC型养老金 随机工资 泊松跳跃过程 工资替代率 

分 类 号：O211.6[理学—概率论与数理统计]