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.