Mean-Variance Portfolio Selection Problem with Stochastic Salary for a Defined Contribution Pension Scheme: A Stochastic Linear-Quadratic-Exponential Framework

Abstract

This paper examines a mean-variance portfolio selection problem with stochastic salary and inflation protection strategy in the accumulation phase of a defined contribution (DC) pension plan. The utility function is assumed to be quadratic. It was assumed that the flow of contributions made by the pension plan members (PPMs) are invested into a market that is characterized by a cash account, an inflation-linked bond and a stock. In this paper, inflation-linked bond is traded and used to hedge inflation risks associated with the investment. The aim of this paper is to maximize the expected final wealth and minimize its variance. Efficient frontier for the three classes of assets that will enable PPMs to decide their own wealth and risk in their investment profile at retirement was obtained. The efficient frontier was found to be parabolic in shape, due to the present of initial capital and the existence of stochastic contributions of the PPM. Some numerical illustration of the analytical results are established in this paper.

Stochastic Funding of a Defined Contribution Pension Plan with Proportional Administrative Costs and Taxation under Mean-Variance Optimization Approach

“…In solving (10), we set ω = ϕ 2ψ and V (t) = X(t) − ω, See [18] for details. As already explained in [18], the problem is equivalent to solving…”

“…Solving the systems of ODEs in (18), (19) and (21) using the boundary conditions, we have the following:…”

“…There have been many studies on the maximization of expected utility of terminal wealth of PPMs in the accumulation phase of defined contribution pension schemes. See, for example, [7,14,4,2,5,9,11,10,8,16,17,18].…”

“…Closely related to this article is a paper by [18], who studied a mean-variance portfolio selection problem with stochastic salary and inflation protection strategy in the accumulation phase of a DC pension plan. The flow of contribution made by PPMs was assumed to be invested into a market that is characterized by a cash account, an inflation-linked bond and a stock.…”

“…In the paper, efficient frontier was found to be parabolic in shape, due to the present of initial capital and the existence of stochastic contributions of the PPM. But, [18] do not addressed wealth and portfolio process with proportional administrative costs and taxation, which we intend to address in this paper. In this paper, administrative cost are those cost incurred in the day-to-day running of the scheme.…”