Optimal Management of DC Pension Plan with Inflation Risk and Tail VaR Constraint

TL;DR

This paper develops a novel approach to optimize pension investments considering inflation risk and tail VaR constraints, deriving explicit solutions and analyzing their impact through numerical simulations.

Contribution

It introduces a new method combining Lagrange and quantile optimization to solve complex pension investment problems with tail VaR constraints.

Findings

Closed-form optimal investment strategies derived.

Tail VaR constraints significantly influence investment decisions.

Numerical results illustrate the impact of constraints on portfolio choices.

Abstract

This paper investigates an optimal investment problem under the tail Value at Risk (tail VaR, also known as expected shortfall, conditional VaR, average VaR) and portfolio insurance constraints confronted by a defined-contribution pension member. The member's aim is to maximize the expected utility from the terminal wealth exceeding the minimum guarantee by investing his wealth in a cash bond, an inflation-linked bond and a stock. Due to the presence of the tail VaR constraint, the problem cannot be tackled by standard control tools. We apply the Lagrange method along with quantile optimization techniques to solve the problem. Through delicate analysis, the optimal investment output in closed-form and optimal investment strategy are derived. A numerical analysis is also provided to show how the constraints impact the optimal investment output and strategy.