This dissertation explores several questions on the topic of pairs trading. The idea of pairs trading isto simultaneously trade a pair of securities, typically stocks. The purpose is to hedge the risk associated with buying and holding shares of a single stock by selling shares of a second stock. This method can be beneficial, because it has the potential to be profitable under any market circumstances. That is to say, it can be profitable even when prices are not going up. The strategy is to track and compare the relative strengths of the prices of two stocks over time. When their prices diverge, the plan is to go long in the weaker stock and go short in the stronger stock. This technique bets on the eventual reversal of their price strengths. The objective is to trade the pairs over time to maximize an overall return with a fixed commission cost for each transaction. The optimal policy is then characterized by threshold curves obtained by solving the Hamilton-Jacobi-Bellman (HJB) equations that arise from following a dynamic programming approach.