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Optimal Portfolio Strategy with Discounted Stochastic Cash Inflows
Department of Mathematics, Faculty of Physical Sciences, University of Benin, Benin City, Nigeria
- 1 Department of Mathematics, Faculty of Physical Sciences, University of Benin, Benin City, Nigeria
Journal of Mathematical Finance·Volume 03 (2013)·Pages 130–137·Published 26 February 2013·DOI10.4236/jmf.2013.31012
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Abstract
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 inflation- linked bond, stock and the cash inflows are stochastic and follow a standard geometric Brownian motion. The vari ational 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.
KeywordsOptimal PortfolioStochastic Cash InflowsInflation-Linked BondVariational FormIntertemporal Hedging Terms
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