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International Journal of Stochastic Analysis
Volume 2012 (2012), Article ID 498050, 8 pages
Research Article

Optimal Geometric Mean Returns of Stocks and Their Options

Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131, USA

Received 23 October 2012; Accepted 9 December 2012

Academic Editor: Qing Zhang

Copyright © 2012 Guoyi Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The optimal geometric mean return is an important property of an asset. As a derivative of the underlying asset, the option also has this property. In this paper, we show that the optimal geometric mean returns of a stock and its option are the same from Kelly criterion. It is proved by using binomial option pricing model and continuous stochastic models with self-financing assumption. A simulation study reveals the same result for the continuous option pricing model.