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University of Paris 13




Dr. Joachim Lebovits


Maître de conférences à  l'Université Paris 13 Nord, membre du LAGA (Laboratoire d'Analyse, Géométrie et applications)

Bureau D 306
99, avenue Jean-Baptiste Clément
93430 - Villetaneuse

Email: joachim.lebovits@math.univ-paris13.fr
Tel: 01 49 40 35 83
Fax : 01 49 40 35 68






Research Interests

  • 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.

Publications

Papers published or to appear (click on the blue link below to get the pdf version of the preprint)

Preprints  

6b. Local Times of Gaussian Processes: Stochastic Calculus wrt Gaussian Processes: Part II, 2017.

6a. Stochastic Calculus with respect to Gaussian Processes: Part I, 2017

6. Stochastic Calculus with respect to Gaussian Processes, 2015, submitted for publication.

Papers published or to appear

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 motionin 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.



Ph.D. Thesis

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.


Other publications

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 ).

(available here).



                                            Referee for Mathematical Journals

- Esaim PS

- Mathematical Finance

                                                                Teaching

At École Centrale Paris, Department of mathematics (M.A.S.): 2008-2011

  • Introduction to measure theory, integration and probability (tutorial)
  • Mathematical finance (tutorial)
  • Stochastic calculus (tutorial).
  • Supervision of many final year projects

At the University René Descartes (Paris V), Department of mathematics (MAP V): 2011-2012 as Temporary Lecturer:

  • Calculus, Analysis and Algebra (tutorials)
  • Computer science (tutorials).
  • Tutorials in basic mathematics for future teachers.

Talks

          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).



Miscellaneous

           Optimal quantization grids used in my paper entitled Multifractional stochastic volatility are available for download on the : Optimal quantization web site


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