A. Zhang, “Stochastic Optimization in Finance and Life Insurance: Applications of the Martingale Method,” Ph.D. Thesis, University of Kaiserslauten, Kaiserslautern, 2007.

has been cited by the following article:

• 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.