This paper examines the variational form of classical portfolio strategy and expected terminal wealth for a Pension Plan Member (PPM) in a Defined Contribution (DC) Pension scheme. The flows of contributions made by PPM are invested into a market that is characterized by a cash account and a stock. It was assumed that the growth rate of salary of PPM is a linear function of time. The present value of PPM’s future contribution process was obtained. The optimal portfolio processes with inter-temporal hedging terms that offset any shocks to the stochastic cash inflows were established. The expected value of PPM’s terminal wealth was obtained

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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.

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.

This paper examines optimal portfolios with discounted stochastic cash inflows (SCI). The cash inflows are invested into a market that is characterized by inflation-linked bond, a stock and a cash account. It was assumed that inflationlinked bond, stock and the cash inflows are stochastic and follow a standard geometric Brownian motion. The variational form of Merton portfolio strategy was obtained by assuming that the investor chooses constant relative risk averse (CRRA) utility function. The inter-temporal hedging terms that offset any shock to the SCI were obtained. A closed form solution to our resulting non-linear partial differential equation was obtained.