STOCHASTIC PORTFOLIO OPTIMIZATION WITH LOG UTILITY

Tao Pang ()
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Tao Pang: Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2006, vol. 09, issue 06, 869-887

Abstract: A portfolio optimization problem on an infinite time horizon is considered. Risky asset price obeys a logarithmic Brownian motion, and the interest rate varies according to an ergodic Markov diffusion process. Moreover, the interest rate fluctuation is correlated with the risky asset price fluctuation. The goal is to choose optimal investment and consumption policies to maximize the infinite horizon expected discounted log utility of consumption. A dynamic programming principle is used to derive the dynamic programming equation (DPE). The explicit solutions for optimal consumption and investment control policies are obtained. In addition, for a special case, an explicit formula for the value function is given.

Keywords: Portfolio optimization; dynamic programming equations; subsolution and supersolutions (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (12)

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DOI: 10.1142/S0219024906003858

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