Formation
Doctorat en Mathématiques Appliquées, Université Paris VI ( effectué en partie au Center for Stochastic Processes, UNC, Chapel Hill, USA)
Post-doctorat (délégation), Cornell University (O.R.I.E.), Ithaca, N.Y., USA
Délégation C.N.R.S. (SAMOS-MATISSE, UMR 8595, 1999-00)
Habilitation à Diriger des Recherches (Commission des Habilitations des Universités Parisiennes et Université Paris I, 2005)
Biographie
Maître de Conférences à l'Université René Descartes, Paris V (UFR de Mathématiques et Informatique) jusqu'en octobre 2006.
Thèmes de Recherche
Thèmes
Probabilité Appliquée et Statistique Mathématique: processus gaussiens (fonctionnelles non linéaires de -), théorie des valeurs extrêmes, processus ponctuels, séries temporelles, systèmes dynamiques, analyse de risque.
Projets en Cours
Working papers: - H. Capa and M.Kratz, Operational Risk Measure in Bayesian context (project partially supported by the ESSEC Research Center).
- S. Das and M. Kratz, On efficiency and alarm system in reinsurance contracts. Papers under review: - A. Estrade, I. Iribarren and M. Kratz, Chord-distribution functions and Rice formulae. Application to random media (Under Revision).
- Y. Demichel, A. Estrade, M. Kratz and G. Samorodnitsky, How fast can the chord-length distribution decay? (preprint).
- A. Guillou, M. Kratz, Y. Le Strat, An Extreme Value Theory approach for the early detection of time clusters with application to the surveillance of Salmonella (arXiv 1003.4466).
- S. Das and M. Kratz, Alarm System for Insurance Companies: A Strategy for Capital Allocation (arXiv 1006.5473) Report: - A.Borchani, Statistiques des valeurs extrêmes dans le cas de lois discrètes (rapport de stage) - (project partially supported by the ESSEC Research Center). Member of MIPOMODIM (Projet ANR blanc - NT05-1_42030) (2006-2009)
Publications académiques
Articles
"Alarm System for Insurance Companies: A Strategy for Capital Allocation" (S. Das, M. Kratz, ), Insurance Mathematics and Economics, mars 2012, Vol. online, Numéro March 2012
"How fast can the chord-length distribution decay?" (Y. Demichel, A. Estrade, M. Kratz, G. Samorodnitsky), Advances in Applied Probability, Numéro 2
"Chord-length distribution functions and Rice formulae. Application to random media" (A. Estrade, I. Iribarren, M. Kratz), Extremes, Numéro July
"Level curves crossings and applications for Gaussian models." (M. Kratz, J. Leon), Extremes, sept. 2009, Vol. 13, Numéro online first
"Level crossings and other level functionals of stationary Gaussian processes" (M. Kratz), Probability Surveys, déc. 2006, Vol. 3, p. 230‑288
"On the second moment of the number of crossings by a stationary Gaussian process" (M. Kratz, J. Leon), Annals of Probability, juil. 2006, Vol. 34, Numéro 4, p. 1601‑1607
"On a representation of Gibbs measure for R.E.M." (M. Kratz, P. Picco), Annals of Applied Probability, mai 2004, Vol. 14, Numéro 2, p. 651‑677
"Central Limit Theorems for Level Functionals of Stationary Gaussian Processes and Fields" (M. Kratz, J. Leon), Journal of theoretical probability, juil. 2001, Vol. 14, Numéro 3, p. 639‑672
"Central limit theorems for the number of maxima and some estimator of the second spectral moment of a stationary Gaussian process. Applications in hydroscience" (M. Kratz, J. Leon), Extremes, mars 2000, Vol. 3, Numéro 1, p. 57‑86
"On the rate of convergence for extremes of mean square differentiable stationary normal processes" (M. Kratz, H. Rootzén), Journal of Applied Probability, déc. 1997, Vol. 34, Numéro 4, p. 908‑923
"Hermite polynomial expansion for non-smooth functionals of stationary Gaussian processes: crossings and extremes" (M. Kratz, J. Leon), Stochastic Processes and their Applications, mars 1997, Vol. 66, Numéro 2, p. 237‑252
"The Q-Q estimator and heavy tails" (M. Kratz, S. Resnick), Stochastic Models, avr. 1996, Vol. 12, Numéro 4, p. 699‑724
"Parameter estimation for moving averages with positive innovations" (M. Kratz, S. Resnick, P. Feigin), Ann. Applied Probab., janv. 1996, Vol. 6, p. 1157‑1190
"Rate of Poisson approximation of the number of exceedances of nonstationary normal sequences" (M. Kratz, J. Hüsler), Stochastic Processes and their Applications, mai 1995, Vol. 55, p. 301‑313
"Approximation Poissonnienne relative du processus empirique" (M. Kratz), C.R.A.S., mai 1993, Vol. 316, série I, p. 1221‑1224
Working papers
"Modelling Macroeconomic Effects and Expert Judgements in Operational Risk: A Bayesian Approach" (H. Capa Santos, M. Kratz, F. Mosquera Munoz). Essec Research Center, DR‑1206 mars 12.
"On Devising Various Alarm Systems for Insurance Companies" (M. Kratz). Essec Research Center, DR‑10008 déc. 10.
Autres publications
Communications publiées
"Fixed points of the Abe formulation of Stochastic Hopfield Networks", avec M. Atencia, G. Joya. In : LNCS 4668, ICANN . Porto (Portugal) : Springer-Verlag, 2007, p. 599-608.
"Stochastic analysis of the Abe formulation of Hopfield networks", avec M. Atencia, G. Joya. In : Proceedings ESANN, ESANN (13th European Symposium on Artificial Neural Networks). Bruges (Belgium) : *, 2005, p. 55-60.
"On the convergence of the number of exceedances of nonstationary normal sequences", avec J. Hüsler. In : Journal of Research of the NIST (National Institute of Standards and Technology), vol 99, Extreme Value Theory and Applications. Gaithersburg, Maryland (USA) : NIST, 1994, p. 539-542.
Enseignement à l'ESSEC
Statistique pour la gestion (PI)
Stochastic methods I : probability in finance (ESSEC MBA) (sections anglaise et française)
Forecasting (Ph.D. DMS) Probability and Stochastic Processes (MSTF Asia & Ph.D) Quantitative Risk Management with the EVT approach (MSTF Asia) Séries temporelles (ISUP-CS3)
Activités scientifiques
Communications présentées à des conférences
"Funcionales de nivel de procesos gaussianos y aplicaciones.", Conferencia Leon: Analisis estadistica y probabilidades, Caracas, Venezuela, 25 nov. 2011
"On a modelization of random porous media.", Ristumeikan and Monash Symposium, Shiga (Kyoto), Japan, 12 sept. 2010
"Operational Risk Measure in Bayesian context. Application in Insurance.", 34th Conference on Stochastic Processes and their Applications, Osaka, Japan, 08 sept. 2010
"EVT in discrete case. Application to disease surveillance. ", Prague Stochastics, Prague, Czechoslovakia, 02 sept. 2010
"On the decay of chord-lengths", Stochastic Processes and their Applications, Berlin, Germany, 30 juil. 2009
"A brief review on EVT basics and operational risk measures", European Workshop on Risk Analysis and EVT, ESSEC, La Défense Paris, France, 26 janv. 2009
"Franchissement de courbe de niveau, formules de Rice et extremum", MAS, SMAI, Rennes, France, 28 août 2008
"On efficiency and alarm system in reinsurance contracts", (avec S. Das). 7th World Congress in Probability and Statistics, IMS and Bernoulli Society, Singapore, Singapore, 14 juil. 2008
"Fixed points of the Abe formulation of Stochastic Hopfield Networks", (avec M. Atencia, G. Joya). 17th ICANN, Porto, Portugal, 10 sept. 2007
"Chord-distribution functions and Rice formulae. Application to random media.", (avec A. Estrade, I. Iribarren). 5th Conference on Extreme Value Analysis, Bern, Switzerland, 27 juil. 2007
"Funciones de distribucion de cuerdas en medios porosos.", (avec A. Estrade, I. Iribarren). Rencontres France-Espagne-Venezuela de probabilité et statistique mathématique, Choroni, Venezuela, 02 nov. 2006
"Curve crossings and specular points, d'après Longuet-Higgins.", (avec J. Leon). 31th Conference on Stochastic Processes and their Applications, Paris, France, 18 juil. 2006
"On level functionals of Gaussian fields", 2nd Intern. Conf. of Applied Mathematics, Plovdiv, Bulgaria, 15 août 2005
"Stochastic analysis of the Abe formulation of Hopfield", (avec M. Atencia, G. Joya). European Symposium on Artificial Neural Networks, Bruges, Belgium, 26 avr. 2005
"Estadisticas de valores extremos", IX Encuentro de Matem\'atica y sus Aplicaciones y IV Seminario de Estad\'istica Aplicada, Quito, Ecuador, 22 juil. 2004
- Co-Organizer of a conference on Financial Regulation - Paris, April 09, 2010
http://isds-department.essec.edu/research/working-group-on-risk/financial-regulation - Organizer of: European workshop on EVT & Finance - Paris La défense, January 26, 2009
/sites/EVTfinance09/ - Co-Organizer of: Workshop on Models and Images for Porous Media - Paris, January 12-16, 2009
http://mipomodim.math-info.univ-paris5.fr/ Affiliations et activités académiques
Affiliations:
Membre de la Bernoulli Society
Membre de la SFdS Vice-présidente avec A.Cohen du groupe BFA (Banque Finance Assurance) de la SFDS Membre du MAP5 (UMR CNRS 8145, Université Paris Descartes) Activités académiques: Organisatrice d'un groupe de travail entre académiques et professionnels sur l'analyse (quantitative) de risque Co-organisatrice du séminaire de recherche du département Conseil
Expérience professionnelle
Maître de Conférences (jusqu'en oct. 2006) en Mathématiques, Université Paris V (UFR de Mathématiques et Informatique).
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