TITLE:
Optimal Portfolio Strategy with Discounted Stochastic Cash Inflows
AUTHORS:
Charles I. Nkeki
KEYWORDS:
Optimal Portfolio; Stochastic Cash Inflows; Inflation-Linked Bond; Variational Form; Intertemporal Hedging Terms
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.3 No.1,
February
28,
2013
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.