Abstract

We investigate the equilibrium behavioral strategy for a defined contribution (DC) pension plan during the accumulation phase in this paper. We adopt a state-dependent function to describe the risk tolerance attitude of a mean-variance (MV) investor, which is a piecewise linear function of the current wealth level with the reference point being the discounted investment target. Meanwhile, the stochastic labor income is taken into account, whose risk sources arise from both financial and non-financial markets. The extended Hamilton-Jacobi-Bellman (HJB) system of equations for our problem is presented. Explicit expressions for the suboptimal equilibrium behavioral strategy and its corresponding equilibrium value function are obtained in the suboptimal sense by the stochastic control technique. We find that the suboptimal equilibrium behavioral strategy takes a piecewise linear feedback form of the current wealth level with respect to the discounted investment target, and it also depends on the current labor income. Finally, some numerical analyses are provided to illustrate the effects of model parameters on the suboptimal equilibrium behavioral strategy and the variance-expectation curve, which shed light on our theoretical results.

摘要

我们在本文的积累阶段研究了固定缴款 (DC) 养老金计划的均衡行为策略。我们采用状态依赖函数来描述均值方差（MV）投资者的风险承受态度，它是当前财富水平的分段线性函数，参考点是贴现投资目标。同时，考虑了随机劳动收入，其风险来源既来自金融市场，也来自非金融市场。针对我们的问题提出了扩展的 Hamilton-Jacobi-Bellman (HJB) 方程组。通过随机控制技术在次优意义上获得了次优均衡行为策略及其对应的均衡值函数的显式表达式。我们发现，次优均衡行为策略对贴现投资目标采取当前财富水平的分段线性反馈形式，并且还取决于当前劳动收入。最后，提供了一些数值分析来说明模型参数对次优均衡行为策略和方差期望曲线的影响，这阐明了我们的理论结果。