Research interests: Malliavin’s calculus; Statistics; Limit Theorems for Gaussian Fields; Stein’s Method; Mathematical Finance – Insurance – Principal-Agent ; Backward Stochastic Differential Equations; Stochastic regularization phenomenon.
– (with J. Martin) A revisit of the Borch rule for the Principal-Agent Risk-Sharing Problem. Submitted.
– (with R. Duboscq) On a stochastic Hardy-Littlewood-Sobolev inequality with application to Strichartz estimates for a noise dispersion. Submitted
Stochastic regularization by noise
– (with R. Duboscq) Stochastic regularization effects of semi-martingales on random functions. Journal de Mathématiques Pures et Appliquées, Vol. 106, No. 6, p. 1141-1173, 2016.
Statistics and Information Theory
– (with N. Privault) SURE shrinkage of Gaussian paths and signal identification. ESAIM Probability and Statistics, Vol. 15, p. 180-196, 2011.
– (with N. Privault) Stein estimation of Poisson process intensities. Statistical Inference for Stochastic Processes, Vol. 12, No. 1, p. 37-53, 2009.
– (with N. Privault) Stein estimation for the drift of Gaussian processes using the Malliavin calculus. The Annals of Statistics, Vol 35, No. 5, p. 2531-2550, 2008.
Limit Theorems for Gaussian Fields – Stein’s Method
– (with Mikko S. Pakkanen) Functional limit theorems for generalized variations of the fractional Brownian sheet. Bernoulli, Vol. 22, No. 3, p. 1671-1708, 2015.
– (with I. Nourdin and G. Peccati) Multivariate normal approximation using Stein’s method and Malliavin calculus. Annales de l’Institut Henri Poincaré série Probabilités et Statistiques, Vol. 46, No. 1, p. 45-58, 2010.
– (with I. Nourdin) Asymptotic behavior of weighted quadratic variations of fractional Brownian motion: the critical case H=1/4. Annals of Probability, Vol. 37, No. 6, p. 2200-2230, 2009.
Mathematical Finance – BSDEs – Insurance
– (with I. Penner) Risk measures for processes and BSDEs. Finance and Stochastics, Vol. 19, No. 1, p. 23-66, 2015.
– (with P. Imkeller and A. Richter) Differentiability of quadratic BSDE generated by continuous martingales and hedging in incomplete markets. Annals of Applied Probability, Vol. 22, No. 1, p. 285–336, 2012.
– (with P. Imkeller and J. Zhang) Solvability and numerical simulation of BSDEs related to BSPDEs with applications to utility maximization. International Journal of Theoretical and Applied Finance, Vol. 14, No. 5, p. 635-667, 2011.
– (with G. dos Reis and J. Zhang) FBSDE with time delayed generators: Lp-solutions, differentiability, representation formulas and path regularity. Stochastic Processes and their Applications, Vol. 121, No. 9, p. 2114-2150, 2011.
– (with M. Jeanblanc) A Note on BSDEs with singular drivers. In « Arbitrage, Credit and Informational Risks ». Proceedings of the Sino-FrenchResearch Program in Financial Mathematics Conference, Beijing June 2013.