Entropic Mean Field Optimal Planning

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The problem of optimal planning was introduced by P.-L. Lions in the context of a mean field game, by fixing a target distribution in the Focker-Planck equation and relaxing the boundary condition in the HJB equation. We analyze an extension of this problem to the path-dependent setting which has remarkable connexions with optimal transport and optimal incentive theory in economics. We provide a general characterization of mean field optimal planning solutions, and we solve explicitly the minimum entropy optimal planning solution.

Brief Biography

Nizar Touzi is a professor of applied mathematics at Ecole Polytechnique since 2006. He was previously Chair Professor at Imperial College London. He received the Louis Bachelier prize of the French Academy of Sciences in 2012 and the Paris Europlace prize of Best Young Researcher in Finance in 2007. In 2010, he held the University of Toronto Dean’s Distinguished Chair position. He is co-editor and associate editor in various international journals in the fields of financial mathematics, applied probability, and control theory.