Université de Paris (anciennement Université Paris Diderot) Laboratoire de Probabilités, Statistiques et Modélisation (LPSM)

Noufel Frikha

Maître de conférences à l'Université de Paris

LPSM UMR 8001
Bâtiment Sophie Germain, 5 rue Thomas Mann
Bureau 541
75013 Paris
phone: (+33)(0) 1 57 27 91 33
e-mail: frikha "abracadabra" math.univ-paris-diderot.fr
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Scientific Interests:


Dilbert.com

Teaching

(2010--2011). A l'Ecole Nationale de la Statistique et de l'Administration Economique :

(2011--2012). A l'Ecole Polytechnique :

(2012--). Responsable pédagogique du Master II ISIFAR, Paris VII :


Publications in refereed journals & Preprints

  1. with J.-F. Chassagneux, J. Chen and C. Zhou (2021): A learning scheme by sparse grids and Picard approximations for semilinear parabolic PDEs, Arxiv version, submitted.
  2. with J. Chen and H. Li (2020): Probabilistic representation of integration by parts formulae for some stochastic volatility models with unbounded drift, Arxiv version, submitted.
  3. with L. Li (2020): Well-posedness and approximation of some one-dimensional Lévy-driven non-linear SDEs, Stochastic Processes and their Applications, Volume 132, February 2021, Pages 76-107.
  4. with S. Menozzi and V. Konakov (2019): Well-posedness of some non-linear stable driven SDEs, Discrete and continuous Dynamical Systems - Series A, February 2021, 41(2): 849-898.
  5. with P.-E. Chaudru de Raynal (2019): From the Backward Kolmogorov PDE on the Wasserstein space to propagation of chaos for McKean-Vlasov SDEs, accepted for publication in Journal de Mathématiques Pures et Appliquées, 59 pages, Arxiv version.
  6. with P.-E. Chaudru de Raynal (2018): Well-posedness for some non-linear diffusion processes and related PDE on the Wasserstein space, under positive revision for Journal de Mathématiques Pures et Appliquées, 124 pages, Arxiv version.
  7. with A. Kohatsu-Higa and L. Li: Integration by parts formula for killed processes: a point of view from approximation theory, (Electronic Journal of Probability), Volume 24, Issue 95, 2019, 1-44.
  8. with L. Li: Weak uniqueness and density estimates for SDEs with coefficients depending on some path-functionals, Ann. Inst. H. Poincaré Probab. Statist. (Annales de l'institut Henri Poincaré ), Volume 56, Number 2 (2020), 1002-1040.
  9. with L. Li: Parametrix method for the first hitting time of an elliptic diffusion with irregular coefficients, 25 pages, published online for (Stochastics). 2020.
  10. On the weak approximation of a skew diffusion by an Euler-type scheme, (arXiv), (Bernoulli), Volume 24, Number 3 (2018), 1653-1691.
  11. with A. Kohatsu-Higa (2015): A Parametrix approach for asymptotic expansion of Markov semigroups with applications to multi-dimensional diffusion processes, 50 pages, submitted.
  12. with L. Huang: A multi-step richardson-romberg extrapolation method for stochastic approximation, (arXiv), (Stochastic Processes and their Applications), Volume 125, Issue 11, November 2015, 4066-4101.
  13. Multi-level stochastic approximation algorithms, (Hal), [Published version]; (The Annals of Applied Probability), Volume 26, Issue 2, April 2016, 933-985.
  14. with M. Fathi: Transport-Entropy inequalities and deviation estimates for stochastic approximation schemes, (Electronic Journal of Probability), Volume 18 (2013), no. 67, 1-36.
  15. with S. Menozzi: Concentration Bounds for Stochastic Approximations, (Electronic Communications in Probability), Volume 17 (2012), no. 47, 1-15.
  16. Shortfall risk minimization in discrete time financial market models , (SIAM Journal on Financial Mathematics), Volume 5, Issue 1, 384-414, (31 pages).
  17. with A. Sagna: Quantization based Recursive Importance Sampling , (Monte Carlo Methods and Applications), 18(4):287-326.
  18. with V. Lemaire: Joint modelling of Gas and Electricity spot prices , (Applied Mathematical Finance), 20(1), 69-93.
  19. with O. Bardou and G. Pagès: CVaR hedging using quantization based stochastic approximation algorithm ,(Mathematical Finance), 26(1):184-229, January 2016.
  20. with O. Bardou and G. Pagès: Computing VaR and CVaR using Stochastic Approximation and Adaptive Unconstrained Importance Sampling , (Monte Carlo Methods and Applications), 15(3):173-210, .
  21. with O. Bardou and G. Pagès: Recursive Computation of Value-at-Risk and Conditional Value-at-Risk using MC and QMC ,(Monte Carlo and Quasi-Monte Carlo Methods 2008), Part 3, 193-208.

Phd Thesis

  1. December (2010): Contribution à la modélisation et à la gestion dynamique du risque des marchés de l'énergie, le manuscrit (HAL), Jury: N. El Karoui, O. Bardou, F.-E. Benth, J.-C. Fort, D. Lamberton, B. Lapeyre, V. Lemaire, G. Pagès.

HDR

  1. November (2017): Stochastic approximation, Markovian perturbation of stochastic processes and their applications., Jury: A. Millet, V. Bally, D. Crisan, F. Delarue, G. Pagès, P. Tankov.

Phd students

  1. Houzhi Li: Study of numerical methods for some stochastic differential equations in finance and modeling of capital distribution in financial market, defended 30th March 2021
  2. Junchao Chen: Theoretical and numerical aspects of some non-linear PDEs in finance: numerical approximation by learning methods and applications in finance domain, expected to be defended at the end of 2021.

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