Dynamic pairs trading using the stochastic control approach

We propose a model for analyzing dynamic pairs trading strategies using the stochastic control approach. The model is explored in an optimal portfolio setting, where the portfolio consists of a bank account and two co-integrated stocks and the objective is to maximize for a fixed time horizon, the expected terminal utility of wealth. For the exponential utility function, we reduce the problem to a linear parabolic partial differential equation which can be solved in closed form. In particular, we exhibit the optimal positions in the two stocks.