Speaker: Gaoyue Guo (Assistant Professor, CentraleSupélec, France)

Title: The most uncertain match

 

Abstract: One of Aldous' open problems is to identify the max-entropy win-probability martingale. Namely, given two players of equal strength, such that the win-probability is a martingale diffusion, which of these processes has maximum entropy and hence gives the most uncertain match. We study a terminal-boundary value problem for the nonlinear parabolic PDE derived by Aldous and prove its well-posedness and regularity of its solution by combining PDE analysis and probabilistic tools. We establish key qualitative properties of the solution including concavity, monotonicity, convergence to a steady state for long remaining time and the asymptotic behavior shortly before the terminal time. This talk is based on the joint-work with Howison, Possamaï and Reisinger.

 

 

Host: Yuming Paul Zhang