Optimal Investment of DC Pension Plan Under Short-Selling Constraints and Portfolio Insurance

Abstract

In this paper we investigate an optimal investment problem with short-selling constraints and portfolio insurance faced by a defined contribution pension fund manager who is loss averse under inflationary risk. The financial market consists of a cash bond, an indexed bond and a stock. The manager aims to maximize the expected S-shaped utility of the terminal wealth exceeding a minimum guarantee. We apply the dual control method to solve the problem and derive the representations of the optimal wealth process and trading strategies in terms of the dual controlled process and the dual value function. We also perform some numerical tests and show how the loss aversion, the short-selling constraints and the portfolio insurance impact the optimal terminal wealth.