Optimal Arbitrage Strategies in Presence of Market Impacts

We consider an arbitrageur who takes advantage of market misvaluations. The market misvaluation is assumed to be mean reverting around zero and to be affected by the arbitrageur's actions. We propose a simple realistic model and explicitly solve the problem and various extensions. We also look at the case where misvaluations are only partially observable. A separation principle is established for that problem: the misvaluation estimation problem and the optimal control problem can be dealt separately