Geodesics for a class of distances in the space of probability measures

2012/04/11 by Pierre Cardaliaguet, Cardaliaguet, Pierre, Guillaume Carlier +3
Economics, Econometrics and Finance · Mathematics · Decision Sciences · #Stochastic processes and financial applications #Point processes and geometric inequalities #Risk and Portfolio Optimization

paper · doi:10.48550/arxiv.1204.2517

Abstract

In this paper, we study the characterization of geodesics for a class of distances between probability measures introduced by Dolbeault, Nazaret and Savar e. We first prove the existence of a potential function and then give necessary and suffi cient optimality conditions that take the form of a coupled system of PDEs somehow similar to the Mean-Field-Games system of Lasry and Lions. We also consider an equivalent formulation posed in a set of probability measures over curves.

Citations

• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem

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