Pairs trading: an optimal selling rule under a regime switching model

This paper is concerned with an optimal selling rule for pairs stock trading. A pairs position consists of a long position in one stock and a short position in the other. The problem is to find an optimal stopping time to close the pairs position by selling the long position and buying back the short position. In this paper, we consider the optimal pairs-trading selling rule by allowing the stock prices to follow a general geometric Brownian motion with regime switching. The optimal policy is characterized by threshold curves obtained by solving the associated HJB equations (quasi-variational inequalities). Moreover, numerical examples are provided to illustrate optimal policies and value functions.