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Probability and Computational Finance Seminar
Francois Delarue Universite Nice Sophia-Antipolis Title: Large population stochastic control and backward SDEs Abstract: I will discuss some results in large population stochastic control, the general philosophy being to investigate the asymptotic behavior of some minimizing functionals set over a large population of interacting stochastic players as the size of the population tends to the infinity. Here I will discuss two types of setting: the first one could be referred to as an "individualist" setting (it is also referred to as "mean field games" in the literature), when each of the player tries to optimize his/her own private cost; the second could be referred to as a "collective" setting, when all the players obey a common policy in order to minimize some common cost. In both cases, I will show that the optimal states can be asymptotically described in terms of forward-backward stochastic differential equations with coefficients of the McKean-Vlasov type. I will give some solvability results and then show the connection with the games driven by a large but finite number of players. This is joint work with Rene Carmona. Date: Monday, April 29, 2013 Time: 5:00 pm Location: Wean Hall 6423 Submitted by: Shreve |