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Abstract
In this paper, we study a mean-variance portfolio selection problem, optimal surplus, minimum pension benefits (MPB) and consumption plan of a defined contribution pension scheme. The problem is formulated as a tri-objective stochastic problem of mean-variance techniques. The problem is solved using dynamic programming approach. The aim of the fund manager is to maximize pension plan member’s (PPM) expected MPB and expected surplus, and at the same time minimize the consumption and portfolio risks. We find the efficient frontier to be nonlinear and parabolic in shape. We further show that the optimal portfolio depend linearly on consumption plan and linearly on MPB. The aggregate optimal pension benefits accrued to a plan member at retirement and life-time consumption of the plan member are obtained. Some numerical illustration of our results were determined.
Highlights
Pension fund management is relatively a long period of time
This paper aims at studying optimal surplus, Minimum Pension Benefits (MPB), optimal total benefit and optimal consumption plan under the context of a defined contribution pension plan with stochastic funding in a DC pension scheme under meanvariance efficient approach. [18] and [37] assumed a constant flow of contributions into the pension scheme which will not be applicable to a time-dependent salary earners in pension scheme
The aggregate pension benefits depend on the shared part of optimal surplus at time, T, the expected value of optimal final surplus that grows as the financial market grows, initial surplus, the contributions of the Pension Plan Member (PPM) which are influence by the market behaviour and consumption rate
Summary
Pension fund management is relatively a long period of time. So, it should be strategically plan to ensure high returns for plan members. We consider a mean-variance portfolio selection problem, optimal surplus, Minimum Pension Benefits (MPB) and optimal consumption plans for a defined contribution pension scheme. We follow the formulation of [38] and [23] but with some modifications toward studying a DC pension plan with the inclusion of investment strategy, the MPB and consumption rate as control variables. [?] examines a mean-variance portfolio selection problem with fixed salary or income and inflation protection strategy in the accumulation phase of a defined contribution pension plan. This paper aims at studying optimal surplus, MPB, optimal total benefit and optimal consumption plan under the context of a defined contribution pension plan with stochastic funding in a DC pension scheme under meanvariance efficient approach.
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