# American Institute of Mathematical Sciences

June  2013, 3(2): 209-231. doi: 10.3934/mcrf.2013.3.209

## Stock trading rules under a switchable market

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

Received  January 2012 Revised  September 2012 Published  March 2013

This work provides an optimal trading rule that allows buying and selling of an asset sequentially over time. The asset price follows a regime switching model involving a geometric Brownian motion and a mean reversion model. The objective is to determine a sequence of trading times to maximize an overall return. The corresponding value functions are characterized by a set of quasi variational inequalities. Closed-form solutions are obtained. The sequence of trading times can be given in terms of various threshold levels. Numerical examples are given to demonstrate the results.
Citation: Duy Nguyen, Jingzhi Tie, Qing Zhang. Stock trading rules under a switchable market. Mathematical Control & Related Fields, 2013, 3 (2) : 209-231. doi: 10.3934/mcrf.2013.3.209
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