Variational Form of Classical Portfolio Strategy and Expected Wealth for a Defined Contributory

Charles I. Nkeki, Chukwuma R. Nwozo

Department of Mathematics, University of Benin, Benin City, Nigeria.
Department of Mathematics, University of Ibadan, Ibadan, Nigeria.

DOI: 10.4236/jmf.2012.21015                

Abstract

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.

Keywords

Variational Form; Classical Portfolio Strategy; Expected Wealth; Defined Contribution; Pension Scheme; Pension Plan Member; Inter-Temporal Hedging Terms; Stochastic Salary

Conflicts of Interest

The authors declare no conflicts of interest.

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