An optimal mean-reversion trading rule under a markov chain model

Jingzhi Tie University of Georgia Qing Zhang University of Georgia

Optimization and Control mathscidoc:1702.27002

MATHEMATICAL CONTROL AND RELATED FIELDS, 6, (3), 2016.9
This paper is concerned with a mean-reversion trading rule. In contrast to most market models treated in the literature, the underlying market is solely determined by a two-state Markov chain. The major advantage of such Markov chain model is its striking simplicity and yet its capability of capturing various market movements. The purpose of this paper is to study an optimal trading rule under such a model. The objective of the problem under consideration is to nd a sequence stopping (buying and selling) times so as to maximize an expected return. Under some suitable conditions, explicit solutions to the associated HJ equations (variational inequalities) are obtained. The optimal stopping times are given in terms of a set of threshold levels. A veri cation theorem is provided to justify their optimality. Finally, a numerical example is provided to illustrate the results.
Mean-reversion Markovian asset, optimal stopping, variational inequalities
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@inproceedings{jingzhi2016an,
  title={AN OPTIMAL MEAN-REVERSION TRADING RULE UNDER A MARKOV CHAIN MODEL},
  author={Jingzhi Tie, and Qing Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170202113522562317153},
  booktitle={MATHEMATICAL CONTROL AND RELATED FIELDS},
  volume={6},
  number={3},
  year={2016},
}
Jingzhi Tie, and Qing Zhang. AN OPTIMAL MEAN-REVERSION TRADING RULE UNDER A MARKOV CHAIN MODEL. 2016. Vol. 6. In MATHEMATICAL CONTROL AND RELATED FIELDS. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170202113522562317153.
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