Optimal Portfolio Strategy with Discounted Stochastic Cash Inflows

Charles I. Nkeki

Department of Mathematics, Faculty of Physical Sciences, University of Benin, Benin City, Nigeria.

DOI: 10.4236/jmf.2013.31012                

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 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.

Keywords

Optimal Portfolio; Stochastic Cash Inflows; Inflation-Linked Bond; Variational Form; Intertemporal Hedging Terms

Conflicts of Interest

The authors declare no conflicts of interest.

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