Optimal Surplus and Minimum Benefits for a Defined Contribution Pension Plan: a Mean-variance Approach

Abstract

In this paper, we study a mean-variance portfolio selection problem, optimal surplus, Minimum Pension Benefits (MPB) and consumption plan of a defined contribution pension scheme. The problem is formulated as a tri-objective stochastic problem of mean-variance techniques. The problem is solved using dynamic programming approach. The aim of the fund manager is to maximize Pension Plan Member's (PPM) expected MPB and expected surplus, and at the same time minimize the consumption and portfolio risks. We find the efficient frontier to be nonlinear and parabolic in shape. We further show that the optimal portfolio depend linearly on consumption plan and linearly on MPB. The aggregate optimal pension benefits accrued to a plan member at retirement and lifetime consumption of the plan member are obtained. Some numerical illustration of our models were obtained.