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 find 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 verification theorem is provided to justify their optimality. Finally, a numerical example is provided to illustrate the results.

中文翻译：

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马尔可夫链模型下的最优均值回归交易规则

本文关注的是均值回归交易规则。与文献中处理的大多数市场模型相比，基础市场完全由二态马尔可夫链决定。这种马尔可夫链模型的主要优点是其惊人的简单性和捕捉各种市场走势的能力。本文的目的就是研究这种模型下的最优交易规则。所考虑问题的目标是找到停止（买入和卖出）时间的序列，以最大化预期回报。在一些合适的条件下，可以获得相关 HJ 方程（变分不等式）的显式解。最佳停止时间是根据一组阈值水平给出的。提供了一个验证定理来证明它们的最优性。最后，