Recherche

Research Interests

  • Pathwise approach to stochastic analysis (in particular rough path theory)
  • Stochastic PDE (singular SPDE, stochastic Hamilton-Jacobi equations)
  • Mathematical finance, in particular rough stochastic volatility models
  • Regularization by noise

Selected presentations

  • Martingale property and moments in signature stochastic volatility models (12/24) slides
  • Gradient flow on control space with rough initial condition (06/24) slides video (fr)
  • Zero noise limit for singular ODE regularized by fractional noise (12/23) slides
  • Complementary Young regularity in Gaussian rough path theory (06/23) slides
  • Stochastic Hamilton-Jacobi equations and their long time behaviour (04/23) slides
  • Reflected SDE and pathwise stochastic analysis (09/22) slides video
  • Weak error rates for rough volatility numerics (12/22) slides

Publications and preprints

  1. Martingale property and moment explosions in signature volatility models, with E. Abi Jaber, D. Sotnikov. Preprint (2025) arXiv
  2. A gradient flow on control space with rough initial condition, with F. Suciu. Preprint (2024). arXiv
  3. Zero noise limit for singular ODE regularized by fractional noise, with Ł. Mądry. Preprint (2024). arXiv
  4. Gaussian Rough Paths Lifts via Complementary Young Regularity, with T. Klose. ECP (2024). arXiv journal
  5. Long-time behaviour of stochastic Hamilton-Jacobi equations, with B. Gess, P.L. Lions, P.E. Souganidis. JFA (2024). arXiv journal
  6. Perturbations of fractional singular SDE, with Ł. Mądry. SPA (2023). arXiv journal
  7. Weak error rates of numerical schemes for rough volatility. SIFIN (2023). arXiv journal
  8. The Neumann problem for fully nonlinear SPDE. with B. Seeger. AAP (2024). arXiv journal
  9. Short dated smile under Rough Volatility: asymptotics and numerics. with P.K. Friz, P. Pigato. Quant. Finance (2022). arXiv journal
  10. Non-uniqueness for reflected rough differential equations. AIHP P&S. (2021). arXiv journal
  11. A Free Boundary Characterisation of the Root Barrier for Markov Processes. with H. Oberhauser, C. Zou. PTRF (2021). arXiv journal
  12. On the martingale property in the rough Bergomi model. ECP (2019). arXiv journal
  13. Precise asymptotics: robust stochastic volatility models. with P.K. Friz, P. Pigato. AAP (2021). arXiv journal
  14. Speed of propagation for Hamilton-Jacobi equations with multiplicative rough time dependence and convex Hamiltonians. with B. Gess, P.L. Lions, P.E. Souganidis. PTRF (2020). arXiv journal
  15. Existence of densities for the dynamic Φ43 model. with C. Labbé. AIHP P&S (2020). arXiv journal
  16. A regularity structure for rough volatility. with C. Bayer, P.K. Friz, J. Martin, B. Stemper Math. Finance (2020). arXiv journal
  17. A stochastic Hamilton-Jacobi equation with infinite speed of propagation. C.R. Mathématiques (2017). arXiv journal
  18. Regularization by noise for stochastic Hamilton-Jacobi equations. with B. Gess PTRF (2019). arXiv journal
  19. Eikonal equations and pathwise solutions to fully non-linear SPDEs. with P.K. Friz, P.L. Lions, P.E. Souganidis. SPDE (2017). arXiv journal
  20. Malliavin Calculus for regularity structures: the case of gPAM. with G. Cannizzaro, P.K. Friz. JFA (2017). arXiv journal
  21. An integral equation for Root's barrier and the generation of Brownian increments. with A.Mijatovic, H. Oberhauser. AAP (2015). arXiv journal
  22. Stochastic control with rough paths. with J. Diehl, P.K. Friz. AMO (2017). arXiv journal
  23. Physical Brownian motion in a magnetic field as a rough path. with P.K. Friz, T.J. Lyons. Transactions AMS (2015). arXiv journal
  24. Root's barrier, viscosity solutions of obstacle problems and reflected FBSDEs. with H. Oberhauser, G. dos Reis. SPA (2015). arXiv journal
  25. Utility maximization with current utility on the wealth: regularity of solutions to the HJB equation. with S. Federico, F. Gozzi. Fin. Stoch. (2017). arXiv journal 
  26. Viscosity characterization of the value function of an investment-consumption problem in presence of illiquid assets. with S. Federico. JOTA (2014). arXiv journal
  27. Impact of time illiquidity in a mixed market without full observation. with S. Federico, F. Gozzi. Math. Finance. (2017). arXiv journal
  28. Time discretization and quantization methods for optimal multiple switching problem. with I. Kharroubi, H. Pham. SPA (2012). arXiv journal 
  29. Investment/consumption problem in illiquid markets with regime-switching. with F. Gozzi, H. Pham. SIAM Control and Optimization (2014). arXiv journal
  30. Optimal investment on finite horizon with random discrete order flow in illiquid markets. with H. Pham, M. Sîrbu. IJTAF (2011). arXiv journal

Theses

  • Habilitation (defended Dec. 2019) pdf
  • PhD thesis (defended Dec. 2011, supervised by Huyên Pham) pdf