 Applied Mathematics, 2011, 2, 912-913 doi:10.4236/am.2011.27123 Published Online July 2011 (http://www.SciRP.org/journal/am) Copyright © 2011 SciRes. AM An Alternative Method of Stochastic Optimization: The Portfolio Model Moawia Alghalith University of the West India, Saint Augustine, Trinidad and Tobago E-mail: malghalith@gmail.com Received May 19, 2011; revised May 26, 2011; accep te d Ma y 29, 2011 Abstract We provide a new simple approach to stochastic dynamic optimization. In doing so, we derive the existing (standard) results using a far simpler technique than the duality and the variational methods. Keywords: Stochastic Optimization, Investment, Portfolio1. Introduction Previous studies in stochastic optimization relied on the duality approach and/or variational techniques such as using the Feynman Kac formula and the Hamilton- Jacobi-Bellman partial differential equations. Examples include [1-3], among many others. In this paper, we offer a new simple approach to stochastic dynamic optimization. That is, we prove the previous results using a simpler method than the duality or the Hamilton-Jacobi-Bellman partial differential equations methods. We apply our method to the standard investment model. Our approach is based on dividing the time horizon into sub-horizons and applying Stein’s lemma. 2. The Portfolio M odel We use the standard investment model (see, for example, , among many others). Similar to previous models, we consider a risky asset and a risk-free asset. The risk-free asset price process is given by where is the rate of return. 0=TrdstSe,2brCRThe dynamics of the risky asset price are given by d=dd ,ss sSS s W (1) where  and  are the deterministic rate of return and the volatility, respectively, and sW is a standard Brownian motion. The wealth process is given by ππ=πdπd,TTTssssssttsXxrXr sW  (2) where x is the initial wealth,  is the risky πstsTportfolio process with . The trading strategy 2πd