An Optimal Trading Rule Under a Switchable Mean-Reversion Model

This work provides an optimal trading rule that allows buying and selling of an asset sequentially over time. The asset price follows a switchable mean-reversion model with a Markovian jump. Such model can be applied to assets with a “staircase” price behavior and yet 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 closedform 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.