Mathematical Finance
Time: 11.00 am
Date: 18th of December 2025
Room 3001

Xin Zhang (NYU) “Exciting games and Monge-Ampère equations”

Abstract: In this talk, we consider a competition between d+1 players, and aim to identify the “most exciting game” of this kind. This is translated, mathematically, into a stochastic optimization problem over  martingales that live on the d-dimensional sub-probability simplex  and terminate on the vertices of the simplex, with a cost function related to a scaling limit of Shannon entropies. We uncover a surprising connection between this problem and the seemingly unrelated field of Monge-Ampère equations, and identify the optimal martingale via a detailed analysis of boundary asymptotics of a Monge-Ampère equation.

Organizers:  Roxanna DUMITRESCU – Jean-François CHASSAGNEUX