Optimal Investment Strategies for DC Pension with Stochastic Salary under the Affine Interest Rate Model

Chubing Zhang,Ximing Rong

doi:10.1155/2013/297875

Abstract

We study the optimal investment strategies of DC pension, with the stochastic interest rate (including the CIR model and the Vasicek model) and stochastic salary. In our model, the plan member is allowed to invest in a risk-free asset, a zero-coupon bond, and a single risky asset. By applying the Hamilton-Jacobi-Bellman equation, Legendre transform, and dual theory, we find the explicit solutions for the CRRA and CARA utility functions, respectively.

Highlights

IntroductionThere are two radically different methods to design a pension fund: defined-benefit plan (hereinafter DB) and definedcontribution plan (hereinafter DC)
There are two radically different methods to design a pension fund: defined-benefit plan and definedcontribution plan
By applying the Hamilton-Jacobi-Bellman equation, Legendre transform, and dual theory, we find the explicit solutions for the constant relative risk aversion (CRRA) and constant absolute risk aversion (CARA) utility functions, respectively

Summary

Introduction

There are two radically different methods to design a pension fund: defined-benefit plan (hereinafter DB) and definedcontribution plan (hereinafter DC). We consider the following framework: (i) the optimal investment strategies are derived with CARA and CRRA utility functions; (ii) the interest rate is affine (including the CIR model and the Vasicek model); (iii) the salary follows a general stochastic process. Under the logarithmic utility function, Gao [2] just studied the portfolio problem of DC with the affine interest rate but did not consider the stochastic salary. The contribution of this paper: (i) extends the research of Gao [2] to the case of the power (CRRA) and exponential (CARA) utility functions under the stochastic salary; (ii) extends the research of Cairns et al [1] to the case of the plan member with the CRRA and CARA utility functions under the affine interest rate model (including the CIR model and the Vasicek model).

Mathematical Model

The Optimization Program

The Legendre Transform

Optimal Investment Strategies with Some Specific Utilities

Conclusions