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.
Cite this paper
C. Nkeki, "Optimal Portfolio Strategy with Discounted Stochastic Cash Inflows," Journal of Mathematical Finance
, Vol. 3 No. 1, 2013, pp. 130-137. doi: 10.4236/jmf.2013.31012
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