Optimal Investment for a Pension Fund Under Inflation Risk

Abstract

This paper investigates an optimal investment problem faced by a defined contribution (DC) pension fund manager under infationary risk. It is assumed that a representative member of a DC pension plan contributes a fixed share of his salary to the pension fund during time horizon [0,T]. The pension contributions are invested continuously in a risk-free bond, an index bond and a stock. The objective is to maximize the expected utility of terminal value of the pension fund. By solving this investment problem we present a way of how to deal with the optimization problem, in the case there is a (positive) endowment (or contribution), using the Martingale method.

Keywords: Pension fund, inflation, optimal portfolio, Martingale method

JEL Classification: C61, G11, G12, G31