Optimal transport, geometry and Monte-Carlo methods for nonlinear PDEs: A ride in mathematical finance.

Authors

HENRY LABORDERE Pierre

Publication date

2014

Publication type

Manuscrit for French Habilitation à Diriger des Recherches (HDR)

Summary 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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Topics of the publication

Optimal transport
Skorokhod embedding problem
Robust hedging
Asymptotic implied volatility
BSDE
McKean
Branching diffusions
...

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