Heston模型中具有保费退回的确定缴费型养老金均衡投资策略

摘要

In this paper,we study the optimal investment problem for the defined contribution(DC)pension plans under the mean-variance criterion.The financial market consists of a risk-free asset and a risky asset with Heston's stochastic volatility(SV).Furthermore,it is assumed that the pension plans have return of premium clauses to protect the rights of the plan members who die during the accumulation phase.By applying a game theoretic framework and solving the extended Hamilton-Jacobi-Bellman(HJB)systems,we derive the explicit expressions of the time-consistent equilibrium strategies,and also the equilibrium efficient frontier.As far as we known,it is the first time to study the equilibrium strategy for DC plans under the Heston's SV model,in which the return of premiums clauses is considered.In the end,some properties of the efficient strategy and the efficient frontier are presented for our results.%本文基于均方差准则研究了Heston模型中确定缴费型养老金(defined contribution,DC)计划的最优投资策略.假定养老金计划可投资于一种无风险资产和一种风险资产(股票),风险资产的价格服从收益率和波动率均为随机的Heston模型.此外,为了保护在基金积累阶段意外死亡的投保人的利益,假定保费可退回(给其继承人).本文在博弈论框架下给出了相应的HJB方程系统,并通过求解相应的HJB方程系统,得到了最优"时间一致"均衡投资策略以及均衡有效前沿的解析式.据我们所知,这是首次在具有保费退回的情形中研究Heston模型中DC计划的均方差均衡投资问题.文章最后分析了最优均衡投资策略和有效前沿的相关性质.