Research

Research interests: Malliavin’s calculus; Statistics; Limit Theorems for Gaussian Fields; Stein’s Method; Mathematical Finance; Backward Stochastic Differential Equations; Stochastic regularization phenomenon.

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To appear

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 – (with  R. Duboscq) Stochastic regularization effects of semi-martingales on random functions. To appear in the Journal de Mathématiques Pures et Appliquées. pdf_3

– (with T. Mastrolia and D. Possamaï) On the Malliavin differentiability of BSDEs. To appear in the Annales de l’Institut Henri Poincaré série Probabilités et Statistiques.pdf_3

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Publications

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Statistics and Information Theory

– Likelihood ratios and Bayesian inference for Poisson channels. IEEE Transactions on Information Theory, Vol. 59, No. 10,  p. 6261-6272, 2013. pdf_3

– (with N. Privault) SURE shrinkage of Gaussian paths and signal identification. ESAIM Probability and Statistics, Vol. 15, p. 180-196, 2011.pdf_3

– Estimation of quadratic variation for two-parameter diffusions. Stochastic Processes and their Applications, Vol. 119, No. 5, p. 1652-1672, 2009. pdf_3

– (with N. Privault) Stein estimation of Poisson process intensities. Statistical Inference for Stochastic Processes, Vol. 12, No. 1, p. 37-53, 2009. pdf_3

– (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. pdf_3

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. pdf_3

– (with M. Stauch and C. A. Tudor)  Hermite variations of the fractional Brownian sheet. Stochastics and Dynamics,  Vol. 12 , No. 3, 2012. pdf_3

– (with I. Nourdin and J. Swanson)  The weak Stratonovich integral with respect to fractional Brownian motion with Hurst index 1/6. Electronic Journal of Probability,  Vol. 15, p. 2117-2162, 2010. pdf_3

– (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. pdf_3

– (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. pdf_3

– Convergence of finite-dimensional laws of the weighted quadratic variations process for some fractional Brownian sheets. Stochastic Analysis and Applications, Vol. 27, No. 1, p. 51-73, 2009. pdf_3

 Mathematical Finance – BSDEs

– (with  P. ImkellerT. Mastrolia and D. Possamaï) A Note on the Malliavin-Sobolev spaces. Statistics and Probability Letters, Vol. 109, p. 45-53, 2016.pdf_3

– (with  T. Mastrolia and D. Possamaï) Density analysis of BSDEs.  Annals of Probability, Vol. 44, No. 4, p. 2817-2857, 2016. pdf_3

– (with  M. JeanblancT. Mastrolia and D. Possamaï) Utility maximization with random horizon: a BSDE approach. International Journal of Theoretical and Applied Finance, Vol. 18, No. 7, 2015. pdf_3

– (with B. Bouchard and R. Elie) BSDES with weak terminal condition. Annals of Probability, Vol. 43, No. 2, p. 572-604, 2015.pdf_3

– (with I. Penner) Risk measures for processes and BSDEs. Finance and Stochastics, Vol. 19, No. 1, p. 23-66, 2015. pdf_3

– (with H. HorstY. HuP. Imkeller,  and J. Zhang) Forward-backward systems for expected utility maximization.  Stochastic Processes and their Applications, Vol. 124, No. 5, p. 1813-1848, 2014. pdf_3

– (with S. Moreno and T. Pirvu)   CRRA Utility Maximization under Risk Constraints.  Communications On Stochastic Analysis,  Vol. 7, No. 2, p. 203-225, 2013.pdf_3

– On the orthogonal component of BSDEs in a Markovian setting. Statistics and Probability Letters, Vol. 82, No. 1, p. 151-157, 2012.pdf_3

– (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. pdf_3

– (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. pdf_3

– (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. pdf_3

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Proceedings

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– (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. pdf_3

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Notes aux Comptes Rendus de l’Académie des Sciences

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– (with N. Privault) Superefficient drift estimation on the Wiener space. CRAS., Vol. 343, p. 607-612, 2006. 

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Technical Reports

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– (with N. Privault) Stochastic analysis on Gaussian space applied to drift estimation.