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Variational Form of Classical Portfolio Strategy and Expected Wealth for a Defined Contributory
Department of Mathematics, University of Benin, Benin City, Nigeria
Department of Mathematics, University of Ibadan, Ibadan, Nigeria
- 1 Department of Mathematics, University of Benin, Benin City, Nigeria
- 2 Department of Mathematics, University of Ibadan, Ibadan, Nigeria
Journal of Mathematical Finance·Volume 02 (2012)·Pages 132–139·Published 28 February 2012·DOI10.4236/jmf.2012.21015
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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.
KeywordsVariational FormClassical Portfolio StrategyExpected WealthDefined ContributionPension SchemePension Plan MemberInter-Temporal Hedging TermsStochastic Salary
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