Equilibrium Investment Strategy for a DC Plan With Partial Information and Mean–Variance Criterion

Abstract

This paper studies a mean–variance portfolio selection problem with partial information for a defined-contribution (DC) pension scheme. We assume that the DC pension plan member can only observe the price of the risky asset but not the appreciation rate of it in the financial market. Moreover, inflation risk and salary risk are taken into account in our model. First, by virtue of the filtering theory, we transform the partially observable mean–variance portfolio selection problem to a completely observable one. Then, to look for an equilibrium investment strategy, we formulate and tackle the mean–variance problem within a game theoretic framework. By solving an extended Hamilton–Jacobi–Bellman (HJB) system of equations, closed-form expressions of the equilibrium investment strategy and corresponding equilibrium value function with partial information are derived for the DC pension plan. In addition, some numerical illustrations are provided to show the effects of parameters on the derived equilibrium investment strategies and the efficient frontier.