Optimal management of DC pension fund under relative performance ratio and VaR constraint

TL;DR

This paper develops an optimal management strategy for DC pension funds considering relative performance, VaR constraints, and inflation risk, providing explicit solutions and numerical insights.

Contribution

It introduces a comprehensive framework combining multiple mathematical methods to derive optimal strategies under complex constraints and inflation considerations.

Findings

Explicit optimal strategies for power penalty and reward functions

Impact of VaR constraints on investment decisions

Numerical illustrations of performance and risk trade-offs

Abstract

In this paper, we investigate the optimal management of defined contribution (abbr. DC) pension plan under relative performance ratio and Value-at-Risk (abbr. VaR) constraint. Inflation risk is introduced in this paper and the financial market consists of cash, inflation-indexed zero coupon bond and a stock. The goal of the pension manager is to maximize the performance ratio of the real terminal wealth under VaR constraint. An auxiliary process is introduced to transform the original problem into a self-financing problem first. Combining linearization method, Lagrange dual method, martingale method and concavification method, we obtain the optimal terminal wealth under different cases. For convex penalty function, there are fourteen cases while for concave penalty function, there are six cases. Besides, when the penalty function and reward function are both power functions, the explicit forms of the optimal investment strategies are obtained. Numerical examples are shown in the end of this paper to illustrate the impacts of the performance ratio and VaR constraint.