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November  2010, 14(4): 1403-1417. doi: 10.3934/dcdsb.2010.14.1403

An optimal trading rule of a mean-reverting asset

Hoi Tin Kong 1, and  Qing Zhang 1,

1. 

Department of Mathematics, University of Georgia, Athens, GA 30602, United States, United States

Received  June 2009 Revised  November 2009 Published  August 2010

This work provides an optimal trading rule that allows buying, selling and short selling of an asset when its price is governed by mean-reverting model. The goal is to find the buy and sell prices such that the overall return (with slippage cost imposed) is maximized. The associated HJB equations (variational inequalities) are used to characterize the value functions. This paper shows that the solution of the original optimal stopping problem can be achieved by solving four algebraic equations. Numerical examples are given for demonstration.
Keywords: mean-reverting process., quasi-variational inequalities, optimal stopping.
Mathematics Subject Classification: Primary: 91G80, 93E20; Secondary: 60G4.
Citation: Hoi Tin Kong, Qing Zhang. An optimal trading rule of a mean-reverting asset. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1403-1417. doi: 10.3934/dcdsb.2010.14.1403
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