le 23 mai 2013 – Université Paris Dauphine – Salle A 707
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15h-16h : Brendan Pass (U. Alberta)
Multi-marginal optimal transport and applications :
Abstract: I will give a general overview of the multi-marginal optimal transport problem and outline several applications. I will try to provide some insight into how and why the uniqueness and structure of solutions differ, depending on the cost function, a phenomenon largely absent in the classical, two marginal problem. -
16h15-17h : João Saúde (LARSyS Lisbon)
Mean field games models :
Abstract: A highly active research area both in mathematics and in applications concerns problem with a very large number of agents.
Mean-field games describe systems with a infinite number of rational agents in competition.
The systematic study of these problems was started, in the mathematical community by Lasry and Lions, and independently
and around the same times in the engineering community by P. Caines and his co-workers.This talk will address two main topics.
In the first one we will briefly cover reduced mean-field games, that is, mean-field games which
are written as a system of Hamilton-Jacobi equation and a transport or Fokker-Plank equation.
Ending with a brief overview of the random variables point of view, as well as some applications to extended mean-field games models.
These models arise in problems where the costs incurred by the agents depend not only on the distribution of the other agents but also on their actions.The second topic of the talk concerns mean-field games on master form.
These mean-field games can be modeled as a partial differential equation in an infinite dimensional space.
We discuss both deterministic models as well as problems where the agents are correlated.
We will end the talk with a mean-field model for price impact.
