Transport optimal, géométrie et méthodes de Monte-Carlo pour EDPs non-linéaires: Une promenade en mathématiques financières.

This habilitation thesis focuses on three parts which are motivated by problems in mathematical finance: (1) martingale optimal transport, (2) asymptotic implied volatility for local and stochastic volatility models using short-time (geometrical) heat kernel expansion and (3) probabilistic numerical schemes for nonlinear parabolic second-order PDEs