Optimal transport, geometry and Monte-Carlo methods for nonlinear PDEs: A ride in mathematical finance
Transport optimal, géométrie et méthodes de Monte-Carlo pour EDPs non-linéaires: Une promenade en mathématiques financières.
Résumé
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.
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