Probability and Financial Mathematics

Team manager: Ahmed Kebaier

Permanent Members

• Five professors: A. Gloter , A. Kebaier , V. Ly Vath , S. Menozzi , Z. Ren

• Four HDR Associate Professors: E. Chevalier , D. Loukianova , C. Profeta , S. Pulido

• Five Associate Professors: A. Barrasso , C. Bénézet , O. Loukianov , J.R. Pycke , A. Sagna

Non-Permanent Members

• One Emeritus Professor: Monique Jeanblanc

• One PAST (Part-Time Lecturer): P. Priaulet

• Four PhD students: A. Paulin , L.M. Boschian-Campaner , M. Fitoussi , Y. Hafsi

The research activity of the team is organized around four areas:

• Stochastic Analysis: stochastic differential equations with singular drift, noise regularization, viscosity solutions for path-dependent partial differential equations, McKean Vlasov equations, singular interaction kernels, interacting particle systems, mean fields, backward stochastic differential equations.

• Numerical Probabilities: Multilevel Monte Carlo methods, approximation schemes for stochastic differential equations with singular coefficients and Volterra-type with singular kernels, numerical solutions for stochastic control problems, optimal quantization, stochastic gradient descent-type algorithms.

• Statistics: statistics of processes and random environments, estimation of stationary measures for anisotropic elliptic processes (with or without jumps) and hypo-elliptic processes, statistical learning (machine learning), mean-field analysis on deep neural networks.

• Financial Mathematics: stochastic modeling based on affine and polynomial processes, weak stochastic target problems, optimal transport, applications to quantile hedging problems, filtration enlargements and applications to derivative pricing, stochastic control, counterparty risk and XVA analysis, model risk, liquidity risk, insurance finance, corporate finance, optimal market making, and order books.

• The seminar page of the PMF team

• 2023– : MATRISK Thematic Network The team is a leading member of the quantitative finance axis.
• 2023– : Financial Risks Chair (A. Kebaier)
• 2021–25: ANR EFFI (A. Gloter and A. Kebaier)
• 2020–24: ANR DREAMeS (A. Kebaier)
• 2018–21: Risk Foundation Program XVA analysis and applications.
• 2017–19: FUI 22 Project, MacroNow: real-time macroeconomics from Big Data led by Quantcube Technology, CACIB, Terranis, and the institutions ENSIIE, Télécom SudParis, and Université Paris-Est (V. Ly Vath).

• Mean field interactions with singular kernels and their approximations, December 18-22, 2023 at IHP, Paris (A. Kebaier and S. Menozzi)
• Dynstoch, June 29 to July 1, 2022 at IHP, Paris (A. Gloter)
• Kolmogorov operators and applications, Cortona 2022 (S. Menozzi)
• Workshop KDE Evry, 2018 (S. Menozzi)

• Kolmogorov operators and their applications. Springer INdAM Series, 56. Springer, Singapore, [2024], (S. Menozzi)
• Statistical Inference for Stochastic Processes (A. Gloter, co-editor-in-chief since 2022)

The team is highly involved in the Master 2 Quantitative Finance (M2QF) program at the Université d'Évry val d'Essonne, specializing in financial mathematics at Paris Saclay since 2015-16, in a double degree with:

• LMU Ludwig-Maximilians-Universität in Munich, Germany, specializing in 'Financial Mathematics Research'.
• UNIBO Alma Mater Studiorum – Università di Bologna, Italy, specializing in 'Statistics and Financial Econometrics'.

2020 : Christophe Profeta, Sergio Pulido

2022 : Bouazza Saadeddine

2023 : Lorenzo Marino , Elizabeth Zuniga , Xavier Erny , Marc Chataigner

2020 : Chiara Amorino

2018 : Florian Rasamoely, Igor Honoré