Optimal execution problem: a mean field game and fictitious play study
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In this work we present the main ideas of the optimal execution problem and a couple of different approaches for its modelling. We focus on the Mean-Field Game approach, and observe how restrictive it can be as we only can obtain a explicit solution for the simplest case. We model a learning algorithm through the concept of the fictitious play, and check that our strategy generated by the model outperforms some different, naive, strategies.