Time-Consistent Investment Strategy for DC Pension Plan with Stochastic Salary Under CEV Model

Abstract

This paper aims to derive the time-consistent investment strategy for the defined contribution (DC) pension plan under the mean-variance criterion. The financial market consists of a risk-free asset and a risky asset of which price process satisfies the constant elasticity of variance (CEV) model. Compared with the geometric Brownian motion model, the CEV model has the ability of capturing the implied volatility skew and explaining the volatility smile. The authors assume that the contribution to the pension fund is a constant proportion of the pension member’s salary. Meanwhile, the salary is stochastic and its volatility arises from the price process of the risky asset, which makes the proposed model different from most of existing researches and more realistic. In the proposed model, the optimization problem can be decomposed into two sub-problems: Before and after retirement cases. By applying a game theoretic framework and solving extended Hamilton-Jacobi-Bellman (HJB) systems, the authors derive the time-consistent strategies and the corresponding value functions explicitly. Finally, numerical simulations are presented to illustrate the effects of model parameters on the time-consistent strategies.