- Gaussian Processes
- Fractional and Multifractional Brownian motion: (fBm) and (mBm)
- Stochastic analysis (stochastic calculus with respect to mBm and Gaussian processes)
- White noise theory
- Mathematical finance.
Papers published or to appear (click on the blue link below to get the pdf version of the preprint)
7. Local Times of Gaussian Processes, 2017.
Stochastic Calculus with respect to Gaussian Processes, 2015, submitted for publication.
Papers published or to appear
6. Stochastic Calculus with respect to Gaussian Processes: Part I, Potential Analysis, 2017
5. Estimation of the global regularity of a multifractional Brownian motion , with Mark Podolskij, in Electronic Journal of Statistics, Vol. 11 (2017), Pages 78-98
4. Stochastic integration with respect to multifractional Brownian motion via tangent fractional Brownian motions, with E.Herbin and J. Lévy-Véhel, in Stochastic Processes and their Applications, Volume 124, Issue 1, January 2014, Pages 678-708
3. Multifractional stochastic volatility, with S.Corlay and J. Lévy-Véhel: Mathematical Finance, Vol. 24, No. 2, April 2014, Pages 364–402
2. From Stochastic integration with respect to fractional Brownian motion to stochastic integration with respect to multifractional Brownian motion, in Annals of the University of Bucharest (mathematical series), 4 (LXII), 2013, pages 397-413
1. White Noise-based Stochastic Calculus with respect to multifractional Brownian, with J. Lévy-Vehel: in Stochastics: An International Journal of Probability and Stochastic Processes: formerly Stochastics and Stochastics Reports, Volume 86, Issue 1, January 2014, pages 87-124.
My PhD Thesis supervisors were Pr. Marc Yor and Dr. Jacques Lévy-Véhel. Entitled "Stochastic Calculus With Respect to Multifractional Brownian Motion and Applications to Finance.", my Ph.D. Thesis has been publicly defended on January 25th, 2012.
1. Nothing personal just business, (2009)
Article about the financial crisis, published in Sept. 2009 in Les Temps Modernes (Political, Philosophical and literary revue founded by J.P. Sartre). (available here).
2. Crise financière et mathématiques, (2009)
Article about the financial crisis, published in Sept. 2009 in Le Diable Probablement n°7 (Political, Philosophical revue ).
Referee for Mathematical Journals
- Esaim PS
- Mathematical Finance
- Introduction to measure theory, integration and probability (tutorial)
- Mathematical finance (tutorial)
- Stochastic calculus (tutorial).
- Supervision of many final year projects
- Calculus, Analysis and Algebra (tutorials)
- Computer science (tutorials).
- Tutorials in basic mathematics for future teachers.
8- August 24-31, 2012. Contributed talk at the 11th French-Romanian colloquim, in Bucarest, (Romania).
7- July 17-19, 2012. Invited at the Seminar “Stochastics”. Responsible Prof. M.Podolskij in Heidelberg (Germany).
6- July 9-14, 2012. Contributed talk at the 8th World Congress in Probability and Statistics, in Istanbul, (Republic of Turkey).
- 5- June 19-24, 2011. Contributed talk at the 35th Conference on Stochastic Processes and their Applications, in Oaxaca, (Mexico).
- 4- May 2, 2011. Invited at the Seminar “Finanzmathematik”. Responsible Prof. W. Schachermayer in Vienna (Austria).
- 3- August 30 - September 3, 2010. Contributed talk at the “Prague Stochastics 2010” conference in Prague (Czech Republic).
- 2- June 21-25, 2010. Contributed talk at the “Journées de Probabilités” conference in Dijon (France).
- 1- May 3-7, 2010. Contributed talk at the “9-ème colloque des jeunes probabilistes et statisticiens” in Le Mont-Dore (France).
Optimal quantization grids used in my paper entitled Multifractional stochastic volatility are available for download on the : Optimal quantization web site