IMPLICATION OF THE KELLY CRITERION FOR MULTI-DIMENSIONAL PROCESSES

Yingdong Lv () and Bernhard K. Meister ()
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Yingdong Lv: Department of Physics, Renmin University of China, Beijing, 100872, China
Bernhard K. Meister: Department of Physics, Renmin University of China, Beijing, 100872, China

International Journal of Theoretical and Applied Finance (IJTAF), 2010, vol. 13, issue 01, 93-112

Abstract: In this paper, we study the Kelly criterion in the continuous time framework building on the work of E.O. Thorp and others. The existence of an optimal strategy is proven in a general setting and the corresponding optimal wealth process is found. A simple formula is provided for calculating the optimal portfolio in terms of drift, short term risk-free rate and correlations for a set of generic multi-dimensional diffusion processes satisfying some simple conditions. Properties of the optimal investment strategy are studied. The paper ends with a short discussion of the implications of these ideas for financial markets.

Keywords: Utility function; Kelly criterion; optimal investment strategy; self-financing; complete market; risk-neutral measure; Brownian motion; Ornstein–Uhlenbeck; diffusion processes; Value-at-Risk (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1142/S0219024910005693

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