## 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**

**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**

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