Stock trading rules under a switchable market

Duy Nguyen; Jingzhi Tie; Qing Zhang

doi:10.3934/mcrf.2013.3.209

Article Contents

2013, Volume 3, Issue 2: 209-231. Doi: 10.3934/mcrf.2013.3.209

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Stock trading rules under a switchable market

1.
Department of Mathematics, University of Georgia, Athens, GA 30602

Received: December 31, 2011

Revised: August 31, 2012

Published: May 2013

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Abstract

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.

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Mathematics Subject Classification: Primary: 93E20, 91B26; Secondary: 49L20.

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References

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