Equilibrium Investment Strategy for DC Pension Plan with Inflation and Stochastic Income under Heston’s SV Model

Jingyun Sun,Yongwu Li,Zhongfei Li

doi:10.1155/2016/2391849

Abstract

We consider a portfolio selection problem for a defined contribution (DC) pension plan under the mean-variance criteria. We take into account the inflation risk and assume that the salary income process of the pension plan member is stochastic. Furthermore, the financial market consists of a risk-free asset, an inflation-linked bond, and a risky asset with Heston’s stochastic volatility (SV). Under the framework of game theory, we derive two extended Hamilton-Jacobi-Bellman (HJB) equations systems and give the corresponding verification theorems in both the periods of accumulation and distribution of the DC pension plan. The explicit expressions of the equilibrium investment strategies, corresponding equilibrium value functions, and the efficient frontiers are also obtained. Finally, some numerical simulations and sensitivity analysis are presented to verify our theoretical results.

Highlights

Nowadays, the application of stochastic control theory to portfolio selection problems of pension funds is becoming a hot issue in actuarial research
If we do not consider the risk of stochastic volatility of the stock price; that is, let α = 0, σV = 0; the equilibrium strategy is simplified as πI∗ (t)
We investigate the MV portfolio problems for a defined contribution (DC) pension plan both before and after retirement

Summary

Introduction

The application of stochastic control theory to portfolio selection problems of pension funds is becoming a hot issue in actuarial research. Some scholars pay attention to the portfolio selection problem of the DC pension plan under the mean-variance (MV) criteria This is because of the fact that the optimal investment problems under the MV criteria in a multiperiod or continuous-time framework are successfully solved only recently. For the MV problem under the background of pension fund, [13] considered a DC pension plan with the return of premiums clauses under the game theoretic framework and obtained an equilibrium investment strategy in the period before retirement. Under the MV criteria, [17] investigated the optimal precommitment investment strategy of a DC pension plan with inflation risk using Lagrange method.

Assumption and Model

Problem Formulation before Retirement and Verification Theorem

Problem Formulation after Retirement and Verification Theorem

Sensitivity Analysis

Findings

Conclusion