Equilibrium investment strategy for multi-period DC pension funds with stochastic interest rate and regime switching

Abstract

This paper studies the equilibrium investment strategy for multi-period defined contribution (DC) pension funds under the mean-variance criterion. We assume that the financial market consists of one risk-free asset and multiple risky assets, the interest rate is stochastic and characterized by the discrete-time Ho-Lee model, and the interest rate as well as the returns of the risky assets both depend on the market states, the evolution of the market states is described by a Markov chain. We regard this problem as a non-cooperative game whose equilibrium strategy is a time-consistent strategy, and derive the analytical expressions for the equilibrium strategy, the equilibrium value function and the equilibrium efficient frontier by using the extended Bellman equation and the matrix representation technique. Finally, a numerical example based on real data from the UK market is provided to shed light on the theoretical results established in this paper.