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An Optimal Trading Rule Under a Switchable Mean-Reversion Model

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Abstract

This work provides an optimal trading rule that allows buying and selling an asset sequentially over time. The asset price follows a switchable mean-reversion model with a Markovian jump. Such a model can be applied to assets with a “staircase” price behavior and yet is simple enough to allow an analytic solution. 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. A closed-form solution is obtained under suitable conditions. The sequence of trading times can be given in terms of a set of threshold levels. Finally, numerical examples are given to demonstrate the results.

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Acknowledgements

We are very grateful to the two referees and the editors for many valuable comments and suggestions, which led to improvements of the paper.

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Authors and Affiliations

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

    Duy Nguyen, Jingzhi Tie & Qing Zhang

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  1. Duy Nguyen
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  2. Jingzhi Tie
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  3. Qing Zhang
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Correspondence to Qing Zhang.

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Nguyen, D., Tie, J. & Zhang, Q. An Optimal Trading Rule Under a Switchable Mean-Reversion Model. J Optim Theory Appl 161, 145–163 (2014). https://doi.org/10.1007/s10957-012-0260-x

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