Education
Main Doctorate in Applied Mathematics, UPMC (Paris 6), done to a great extent at the Center for Stochastic Processes, UNC, Chapel Hill, USA Habilitation à Diriger des Recherches, Commission des Thèses en Mathématiques des Universités Parisiennes & Université Paris I Additional Global colloquium on participant-centered learning, Harvard Business School (Executive Education) (July 25- Aug.04, 2010; March14-18, 2011) Ecole d'été de Probabilités de Saint-Flour (R. Adler & A. Etheridge lectures) (July 5-17, 2009) From classical to Modern Probability, CIMPA & CMM summer school, Universidad de la Frontera, Temuco, Chile (Jan. 2001) Summer Internships Program in Probability and Stochastic Processes, University of Wisconsin, Madison, U.S.A. (J. Kuelbs and T. Kurtz) (July 1999)
Biography
ESSEC Full Professor, from Oct. 2011 Director of CREAR - Center of Research in Econo-finance and Actuarial Science on Risk - (see http://crear.essec.edu), from Jan. 2013 ESSEC Associate Professor, Oct. 2006 - Sept. 2011 Maître de Conférences at the University René Descartes Paris V (UFR Mathématiques & Informatique) until Oct. 2006 Delegation C.N.R.S. (SAMOS-MATISSE, UMR 8595, 1999-2000) Post-doctorat/delegation with S. Resnick (Fall sem. 1993, 94, 95), Cornell University (O.R.I.E.), Ithaca, N.Y., USA
Research Areas
Areas
Quantitative Risk Analysis; Extreme Risks; Extreme Value Theory; Gaussian processes (non linear functionals); Stochastic Geometry; Point Processes; Time Series; Dynamical Systems
Sectors
Applied Probability; Mathematical Statistics; Actuarial Mathematics; Risk Management
On-going Projects
On-going papers (presented at International Conferences): A. Banerjee, G. Chevillon and M. Kratz, Detecting and Forecasting Asset Price Bubbles using a Near-Explosive Random Coefficient Autoregressive Model M. Kratz, There is a VaR beyond usual approximations M. Kratz and W. Nagel, Tail distribution of functionals of random excursion sets L. Elbahtouri, M. Dacorogna, M.Kratz, Explicit diversification benefit formulas for dependent risks Director of the Research Program with SWISS LIFE on : Consequences of the population ageing on the insurances loss. Impacts on the automobile prevention (Dec 11 - Dec 13) Scientific Coordinator of the ”Risk Analysis and Modeling” direction, in the European Project RARE - Risk Analysis, Ruin and Extremes - FP7-PEOPLE-2012-IRSES - Marie Curie Actions, which aims to strengthen research partnerships through staff exchanges and networking activities between European research organizations and research organizations from other countries. (12 partners) (Oct 12 - Oct16) Papers under review: A. Guillou, M. Kratz and Y. Le Strat, EVT in discrete case. Application to disease surveillance. Reports: 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) A.Borchani, Statistiques des valeurs extrêmes dans le cas de lois discrètes (rapport de stage) - (project partially supported by the ESSEC Research Center).
Academic Publications
Articles
"Modelling macroeconomic effects and expert judgements in operational risk : a Bayesian approach" (H. Capa Santos, M. Kratz, F. Mosquera M), Journal of Operational Risk, Dec 2012, Vol. 7, Issue Winter 2012-2013, p. 3‑23
"Alarm System for Insurance Companies: A Strategy for Capital Allocation" (S. Das, M. Kratz, ), Insurance Mathematics and Economics, Mar 2012, Vol. online, Issue March 2012
"How fast can the chord-length distribution decay?" (Y. Demichel, A. Estrade, M. Kratz, G. Samorodnitsky), Advances in Applied Probability, Issue 2
"Chord-length distribution functions and Rice formulae. Application to random media" (A. Estrade, I. Iribarren, M. Kratz), Extremes, Issue July
"Level curves crossings and applications for Gaussian models." (M. Kratz, J. Leon), Extremes, Sep 2009, Vol. 13, Issue online first
"Level crossings and other level functionals of stationary Gaussian processes" (M. Kratz), Probability Surveys, Dec 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, Jul 2006, Vol. 34, Issue 4, p. 1601‑1607
"On a representation of Gibbs measure for R.E.M." (M. Kratz, P. Picco), Annals of Applied Probability, May 2004, Vol. 14, Issue 2, p. 651‑677
"Central Limit Theorems for Level Functionals of Stationary Gaussian Processes and Fields" (M. Kratz, J. Leon), Journal of theoretical probability, Jul 2001, Vol. 14, Issue 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, Mar 2000, Vol. 3, Issue 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, Dec 1997, Vol. 34, Issue 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, Mar 1997, Vol. 66, Issue 2, p. 237‑252
"The Q-Q estimator and heavy tails" (M. Kratz, S. Resnick), Stochastic Models, Apr 1996, Vol. 12, Issue 4, p. 699‑724
"Parameter estimation for moving averages with positive innovations" (M. Kratz, S. Resnick, P. Feigin), Ann. Applied Probab., Jan 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, May 1995, Vol. 55, p. 301‑313
"Approximation Poissonnienne relative du processus empirique" (M. Kratz), C.R.A.S., May 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 Mar 12.
"On Devising Various Alarm Systems for Insurance Companies" (M. Kratz). Essec Research Center, DR‑10008 Dec 10.
"Some contributions in probability and statistics of extremes" Université Paris 1 , HAL : tel-00239329 Nov 05.
"Chaos expansions and level crossings" Univ. Paris 1, Samos 127 Sep 00.
"Statistics of tails of distributions and Poisson approximation" UPMC Paris 6, 93 Mar 93. (Doctorate thesis in Applied Mathematics - UPMC (Paris 6))
Other Publications
Articles published in conference proceedings
"Combining algebraic approach with extreme value theory for spike detection", With N. Debabbi, M. Mboup, S. El Asmi. In : Proceedings of EUSIPCO 2012, 20th European Signal Processing Conference. : IEEE Conference Publications Program, 2012, p. 1836-1840
"Fixed points of the Abe formulation of Stochastic Hopfield Networks", With 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", With 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", With 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
Teaching at ESSEC
Financial Mathematics : Probability in finance (Ms ESSEC Grande Ecole)
Gestion des risques (ISUP Univ. Paris 6 - CS3 - Actuarial track) (from 2011-12) Séries temporelles (ISUP Univ. Paris 6 - CS2) (2006-07 to 2010-11) Forecasting (Ph.D. OMS) Probability and Stochastic Processes (MS FEAsia & Ph.D) Statistics (MS FEAsia) Quantitative Risk Management (QRM) (Ms ESSEC Grande Ecole) QRM & Extreme values (MS FEAsia Singapore) Research UE on QRM Statistics in Business (Bachelor) (from 2007 to 2009) (coordinator from 2008 to 2011)
Scientific Activities
Conference Presentations
"There is a VaR beyond usual approximations", Workshop on Heavy-tailed Distributions and Extreme Value Theory, Indian Statistical Institute (ISI), Kolkata, India, 15 Jan 2013
"Tail distribution of functionals of random excursion sets", (with W. Nagel). Stereology, Spatial Statistics and Stochastic Geometry (S4G), Charles University Prague, Prague, Czech Republic, 28 Jun 2012
"Tail distribution of functionals of random excursion sets", (with W. Nagel). International Workshop on Applied Probability (IWAP), Jerusalem, Israël, 13 Jun 2012
"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 Sep 2010
"Operational Risk Measure in Bayesian context. Application in Insurance.", 34th Conference on Stochastic Processes and their Applications, Osaka, Japan, 08 Sep 2010
"EVT in discrete case. Application to disease surveillance. ", Prague Stochastics, Prague, Czechoslovakia, 02 Sep 2010
"On the decay of chord-lengths", Stochastic Processes and their Applications, Berlin, Germany, 30 Jul 2009
"A brief review on EVT basics and operational risk measures", European Workshop on Risk Analysis and EVT, ESSEC, La Défense Paris, France, 26 Jan 2009
"Franchissement de courbe de niveau, formules de Rice et extremum", MAS, SMAI, Rennes, France, 28 Aug 2008
"On efficiency and alarm system in reinsurance contracts", (with S. Das). 7th World Congress in Probability and Statistics, IMS and Bernoulli Society, Singapore, Singapore, 14 Jul 2008
"Fixed points of the Abe formulation of Stochastic Hopfield Networks", (with M. Atencia, G. Joya). 17th ICANN, Porto, Portugal, 10 Sep 2007
"Chord-distribution functions and Rice formulae. Application to random media.", (with A. Estrade, I. Iribarren). 5th Conference on Extreme Value Analysis, Bern, Switzerland, 27 Jul 2007
"Funciones de distribucion de cuerdas en medios porosos.", (with 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.", (with J. Leon). 31th Conference on Stochastic Processes and their Applications, Paris, France, 18 Jul 2006
"On level functionals of Gaussian fields", 2nd Intern. Conf. of Applied Mathematics, Plovdiv, Bulgaria, 15 Aug 2005
"Stochastic analysis of the Abe formulation of Hopfield", (with M. Atencia, G. Joya). European Symposium on Artificial Neural Networks, Bruges, Belgium, 26 Apr 2005
"Estadisticas de valores extremos", IX Encuentro de Matem\'atica y sus Aplicaciones y IV Seminario de Estad\'istica Aplicada, Quito, Ecuador, 22 Jul 2004
- Organizer of a Working Group on RISK ANALYSIS - ESSEC La Défense, since Oct. 2009 Meetings: twice a month (seminars and/or discussions on projects) Since March 2012, it has been acknowledged by the French Institute of Actuaries as part of its continuous education program see http://isds-department.essec.edu/research/working-group-on-risk and, since 2013, http://crear.essec.edu/research/working-group-on-risk - Co-Organizer (ESSEC Working Group on Risk - SWISS LIFE) conference on Risk, Insurance and Longevity, ESSEC La Défense, November 19, 2012 http://risk-insurance-longevity-event.essec.edu - Co-Organizer (BFA Group of SFdS - ESSEC Working Group on Risk) of a conference on Financial Regulation - Paris, April 09, 2010 http://isds-department.essec.edu/research/working-group-on-risk/financial-regulation - Co-Organizer of a 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 and Academic Responsibilities
Academic Responsibilities: - Director of CREAR - Center of Research in Econo-finance and Actuarial sciences on Risk ; see http://crear.essec.edu - Organizer of a working group with academics and professionals on (quantitative) risk analysis - Director of the research program ESSEC - SWISS LIFE "Consequences of the population ageing on the insurances loss. Impacts on the automobile prevention" Dec 2011 Dec 2013 - Scientific Coordinator of the ”Risk Analysis and Modeling” direction, in the European Project ‘RARE’ - Risk Analysis, Ruin and Extremes - FP7-PEOPLE-2012-IRSES - Marie Curie Actions, which aims to strengthen research partnerships through staff exchanges and networking activities between European research organizations and research organizations from other countries. (12 partners) (Oct 2012 - Oct. 2016) - Director of the ESSEC-ISUP actuarial track (from Oct. 2012) - Co-responsible of the ESSEC-ISUP actuarial track (Oct. 2008 - Oct. 2012) - Co-organizer of the IDS department research seminar - President of the Banque, Finance, Assurance (BFA) group - SFdS Supervising Activities of: - Doctoral Students - L. Elbahtouri (UPMC-SCOR): ``Diversification and heavy tailed distributions'' (since Oct.10); co-dir. with M. Dacorogna (Group Deputy CRO, SCOR) - N. Debbabi (URCA): "Approche algébrique et théorie des valeurs extrêmes pour la détection de ruptures: application aux signaux biomédicaux" (since Dec.10); co-dir. with M. Mboup (Prof. URCA) and S. El Asmi (Prof. SUPCOM Tunis) - M. Cadena (UPMC-ESSEC-SWISS LIFE): ``Contributions actuarielles et statistiques pour l'analyse de risques en assurance liés au vieillissement de la population, notamment en assurance automobile " (since Feb. 13) - Master (or equivalent) Students - Research training at ESSEC and SWISSLIFE from May to November 12 for two Master students (ISFA, Lyon) (final training study to validate their diploma, one for a Research Master, the other for a Professional Master for the title of Actuary) on the "Consequences of the population ageing on the insurances loss. Impacts on the automobile prevention" - Research training at ESSEC from Feb. to May 2008 for an engineer student (ESSAI, Tunis) (final training study to validate his diploma) on "Extreme Value Theory for discrete random variables, with applications in Epidemiology and in Finance" - Paris Descartes Master students final professional trainings from 1997-98 to 2005-06 (MST2-ISASH, DESS MSB, Master 2 IMSV) Affiliations: BERNOULLI SOCIETY (for Mathematical Statistics and Probability- ISI section) SFdS - Société Française de Statistique MAP5 (Applied Mathematics), UMR8145, Univ. Paris Descartes GDR 3477 (CNRS) - Géométrie Stochastique - see http://gdr-geostoch.math.cnrs.fr Member of MIPOMODIM (Projet ANR blanc - NT05-1_42030) (2006-2009) Consulting & Other Activities
Professional Experience
Maître de Conférences (until Oct. 2006) in Mathematics, Université Paris Descartes (UFR Mathématiques & Informatique) Internship at FINMA- Swiss Financial Market Supervisory Authority- Zürich, July-Dec 2012
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