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Research Interests
Applied Probability, Financial Mathematics, Numerical analysis.
Probabilistic numerical methods for non-linear PDEs, Stochastic Analysis, Backward Stochastic Differential Equation (BSDE), Large Population Stochastic Control, Non linear pricing methods, Market with imperfections.
Publications
Books
- Fundamentals and Advanced Techniques in Derivatives Hedging with B. Bouchard, Springer, Universitext, 2016. (first french edition: Economica, 2014)
- A Forward-Backward SDEs Approach to Pricing in Carbon Markets with H. Chotai and M. Muuls, SpringerBriefs in Mathematics of Planet Earth, 2017.
- A probabilistic approach to classical solutions of the master equation for large population equilibria with D. Crisan and F. Delarue, Memoirs of the AMS, 2022. (preprint)
Articles
- Preprints
- Accepted papers
- Other:
Computing the invariant distribution of McKean-Vlasov SDEs by ergodic simulation with G. Pagès arXiv:2406.13370.
An optimal transport approach for the multiple quantile hedging problem with C. Bénézet and M. Yang, arXiv:2308.01121.
Propagation of carbon tax in credit portfolio through macroeconomic factors with G. Bouveret, S. Ibbou, A. Jacquier and L. Sopgoui, arXiv:2307.12695.
Convergence of particles and tree based scheme for singular FBSDEs with M. Yang, arXiv:2212.11917.
Deep Runge-Kutta schemes for BSDEs with J. Chen and N. Frikha, arXiv:2212.14372.
Numerical approximation of singular Forward-Backward SDEs (2022) with M. Yang, Journal of Computational Physics, 468. (preprint)
A learning scheme by sparse grids and Picard approximations for semilinear parabolic PDEs (2022) with J. Chen, N. Frikha and C. Zhou, IMA Journal of Numerical Analysis. (preprint)
Reflected BSDEs in non-convex domains (2022) with S. Nadtochiy and A. Richou, Probability Theory and Related Fields,183, pages 1237–1284. (preprint)
Modelling multi-period carbon markets using singular forward backward SDEs with H. Chotai and D. Crisan, forthcoming in Mathematics of Operations Research (preprint).
Weak quantitative propagation of chaos via differential calculus on the space of measures (2022) with L. Szpruch and A. Tse, Annals of Applied Probability, 32(3), 1929-1969. (preprint).
Switching problems with controlled randomisation and associated obliquely reflected BSDEs (2022) with C. Bénézet and A. Richou, Stochastic Processes and their Applications, 144, 23-71. (preprint).
A numerical scheme for the quantile hedging problem (2021) with C. Bénézet and C. Reisinger, SIAM Journal on Financial Mathematics 12(1), 110-157. (preprint)
Obliquely Reflected BSDEs (2020) with A. Richou, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques , 56(4), 2868-2896. (preprint)
Cubature methods to solve BSDEs: Error expansion and complexity control (2020) with C. Garcia Trillos, Mathematics of Computation. (preprint)
Rate of convergence for the discrete-time approximation of reflected BSDEs arising in switching problems (2019) with A. Richou, Stochastic Processes and their Applications, 119(11), 4597-4637. (preprint)
Numerical Method for FBSDEs of McKean-Vlasov Type (2019) with D. Crisan and F. Delarue, Annals of Applied Probability, 29(3), 1640-1684. (preprint)
A sparse grid approach to balance sheet risk measurement (2019) with C. Bénézet, J. Bonnefoy, S. Deng, C. Garcia Trillos and L. Lenôtre, in ESAIM: ProcS 65, 236-265. (preprint)
Numerical Probabilistic Approach to MFG (2019) with A. Angiuli, C. Graves, H. Li, F. Delarue and R. Carmona, in ESAIM: ProcS, 65, 84-113. ( preprint )
A comparison principle for PDEs arising in approximate hedging problems: application to Bermudan options (2018), with G. Bouveret, in AMO, 78, 469-491. (preprint)
An explicit Euler scheme with strong rate of convergence for non-Lipschitz SDEs (2016), with A. Jacquier and I. Mihaylov, SIAM J. Finan. Math., 7(1), 993-1021. (preprint)
A backward dual representation for the quantile hedging of Bermudan options (2016), with B. Bouchard and G. Bouveret, SIAM J. Finan. Math., 7(1), 215-235. (preprint)
Numerical simulation of quadratic BSDEs (2016), with A. Richou, Ann. Appl. Probab., 26(1), 262-304.(preprint)
Numerical stability analysis of the Euler scheme for BSDEs (2015), with A. Richou, SIAM J. Numer. Anal., 53(2), 1172–1193.(preprint)
When terminal facelift enforces Delta constraints (2015), with R. Elie and I. Kharroubi, Finance and Stochastics, 19(2), 329-362.(preprint)
Linear multi-step schemes for BSDEs (2014), SIAM J. Numer. Anal., 52(6), 2815–2836.(preprint)
Runge-Kutta schemes for BSDEs (2014), with D. Crisan, Ann. Appl. Probab., 24(2), 679-720.(preprint)
Doubly reflected BSDEs with call protection and their approximation (2014), with S. Crépey, ESAIM: Probability and Statistics,18, 613-641.(preprint)
Discrete-time approximation of multidimensional BSDEs with oblique reflections (2012), with R. Elie and I. Kharroubi, Annals of Applied Probability, 22(3), 971-1007.(preprint)
A note on existence and uniqueness for solutions of multidimensional reflected BSDEs (2011), with R. Elie and I. Kharroubi, Electronic Communications in Probability, 16, 120-128.(preprint)
A discrete-time approximation for doubly reflected BSDE (2009) , Advances in Applied Probability, 41(1), 101-130.(preprint)
Representation of continuous linear forms on the set of ladlag processes and the pricing of American claims under proportional costs (2008), with B. Bouchard, Electronic Journal of Probability, 14, 612-632 .(preprint)
Discrete-time approximation for continuously and discretely reflected BSDEs (2008), with B. Bouchard, Stochastic Processes and their Applications, 118(12), 2269-2293.(preprint)
Wind in Ireland: seasonality or long memory (2006), with J.C. Bouette, D. Sibai, R. Terron and A Charpentier, Stochastic Environmental Research & Risk Assessment, vol 20.3, pp 141-151.
HDR thesis (2014) Quelques contributions à la finance mathématique et à l'analyse théorique et numérique des EDSR, Université d'Evry - Val d'Essonne.
PhD thesis (2008) Processus réfléchis en finance et probabilité numérique: Régularités et approximation d'EDSR réfléchies et Options américaines en présence de coûts de transaction, Université Paris Diderot - Paris 7.
Events & Seminars
Past events:- London-Paris Bachelier workshop, 18 and 19 September 2023, Imperial College London.
- Monte Carlo Methods and Applications, 26-30 June 2023, Sorbonne Université.
- Workshop ANR project Mean Field Games, 17 and 18 December 2018, Université Paris Diderot.
- Workshop on Risk Management , 9 October 2018, AXA.
- CEMRACS 2017. Numerical methods for stochastic models: control, uncertainty quantification, mean-field. July 17 - August 25 2017, CIRM, Marseille.
- 2nd USPC-NUS Workshop on New Challenges in Financial Risk Control, April 11-12 2017, at National University of Singapore.
- USPC-NUS Workshop on models and numerical methods for financial risk management, on October 6 - October 7 2016 at Université Paris Diderot.
- Workshop on 'Probabilistic numerical methods for non-linear PDE' at Imperial College London on the 29th, 30th of June and 1st of July 2015.