通货膨胀风险下关于累积阶段的固定缴费养老金的均值-方差问题

Dynamic mean-variance problem for de?ned contribution pension fund under in?ation

本文研究了在通货膨胀环境下关于累积阶段的固定缴费(de?ned contribution, DC)养老金的一个均值-方差问题.一般来说, DC养老金的管理周期比较长,所以,本文考虑了养老金的实际财富过程,而非名义财富过程,并且假设价格指数的动态过程包含一个跳-扩散过程.通过投资金融市场上的三种产品(无风险银行账户、通胀指数债券和风险资产),该DC养老金最优管理的目标是在给定期望的前提下最小化终端时间的方差.风险资产同样包含一个跳-扩散过程.通过解相关的Hamilton-Jacobi-Bellman (HJB)方程,本文得到了最优的投资策略以及相关的有效前沿的显式表达.

This paper studies the optimal investment strategy for a mean-variance problem of a defined contribution(DC)pension plan during the accumulation phase.Generally,the time horizon of DC pension management is really long,and thus the real wealth process,instead of the nominal process is derived with the consideration of inflation.The inflation index is described by a jump-diffusion process.The plan aims to minimize the risk measured by variance,by investing the wealth in a financial market consisting of a bank account,an inflation-indexed bond and a risky asset.The dynamic of the risky asset is also subjected to a Poisson jump and a Brownian uncertainty.The closed-form optimal investment decision and the efficient frontier are derived by solving the corresponding Hamilton-Jacobi-Bellman(HJB)equation.