A closed-form solution for optimal mean-reverting trading strategies

The heat potentials method is used to find the optimal profit-taking and stop-loss levels

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All market makers are confronted with the problem of defining profit-taking and stop-out levels. More generally, all execution traders holding a particular position for a client must determine at what levels an order needs to be fulfilled. Those optimal levels can be ascertained by maximising the trader’s Sharpe ratio in the context of Ornstein-Uhlenbeck processes via Monte Carlo experiments. In this article, Alex Lipton and Marcos Lopez de Prado develop an analytical