Le groupe de travail Valeurs Extrêmes et Longévité a lieu deux fois par mois : une séance sur le thème de la théorie des valeurs extrêmes et une séance sur le thème de la longévité

 Vendredi à 13h45 
Université Pierre et Marie Curie
4 place Jussieu 75005 Paris (Métro Jussieu)

Valeurs extrêmes : Nathalie Akakpo, Philippe Naveau, Maud Thomas et Olivier Wintenberger
Longévité :  Nicole El Karoui, Caroline Hillairet, Sarah Kaakai et Olivier Lopez

Prochaines séances
Vendredi 19 Janvier
** Séance d'1h30 - !! Attention salle 15-16 101 !! **
Thomas Mikosch (University of Copenhagen, Danemark) Heavy tails for an alternative stochastic perpetuity model
This is joint work with M. Rezapour (Kerman) and O. Wintenberger (Paris). We consider a stochastic model of perpetuity-type. In contrast to the classical affine perpetuity model of Kesten (1973) and Goldie (1991) all discount factors in the model are mutually independent. We prove that the tails of the distribution of this model are regularly varying both in the univariate and multivariate cases. Due to the additional randomness in the model the tails are not pure power laws as in the Kesten-Goldie setting but involve a logarithmic term.
Hrovje Planinic (University of Zagreb, Croatie) -  Local sequence alignment and compound Poisson approximation
This is joint work with prof. Bojan Basrak (University of Zagreb). We study (ungapped) local alignments with score of two independent i.i.d. sequences of letters from a finite alphabet, see Dembo, Karlin and Zeitouni (1994) and also Hansen (2006). It is known that the maximum local alignment score, under certain conditions, is asymptotically Gumbel distributed. This result can be used to test similarity between two biological sequences. To show convergence of the maximum, the basic idea is to count the number of essentially different local alignments with score bigger than a suitably chosen high treshold and show that it converges to a Poisson random variable, where the Poisson approximation relies on the well known result from Arratia, Goldstein and Gordon (1989).
We show that it is possible to obtain a Poisson cluster limit for the point process of all local alignment scores together with their locations. As a simple consequence, one gets a compound Poisson approximation for the number of all local alignments with score exceeding a high treshold. The proof of the point process convergence is based on a new point process version of the result from of Arratia et al. (1989) and 
extension of the work on stationary regularly varying time-series from Basrak, Planinic, Soulier (2016), to the case of random fields on the two-dimensional integer lattice.
Jean-Marc Bardet (Université Paris Sorbonne) - A new non-parametric detector of univariate outliers for distributions with unbounded support
The purpose of this paper is to construct a new non-parametric detector of univariate outliers and to study its asymptotic properties. This detector is based on a Hill's type statistic. It satisfies a unique asymptotic behavior for a large set of probability distributions with positive unbounded support (for instance: for the absolute value of Gaussian, Gamma, Weibull, Student or regular variations distributions). We have illustrated our results by numerical simulations, which show the accuracy of this detector with respect to other usual univariate outlier detectors (Tukey, MAD or Local Outlier Factor detectors). The detection of outliers in a database providing the prices of used cars is also proposed as an application to real-life database.

Vendredi 26 janvier - salle 16-26 Salle 113
Sebastian Mentemeier (TU Dortmund) Extremal paths of nonlinear time series
When observing time series (stock prices, exchange rates, weather data), extremal behavior is often much more exciting than "regular" behavior. Conditioned on the occurence of an extreme event, how does the path of the time series leading to or from this extreme event look like? How is it different from a non-extreme path? Can one identify universal behavior close to extreme values?In this talk, I'm going to answer these questions in the context of GARCH processes by means of conditional limit theorems.  The talk is based on joint work with  Jeffrey Collamore (Copenhagen).

Vendredi 2 Février - salle 16-26 Salle 113
** Séance d'1h30 **
Dan Cooley (Colorado's State University, USA) - TBA
Bojan Basrak (University of Zagreb, Croatie) - TBA

Vendredi 9 Mars - salle 16-26 Salle 113
Johannes Heiny (Aarhus University) - TBA

Vendredi 6 Avril - salle 16-26 Salle 113
Clément Albert (INRIA Grenoble) - TBA

Séance reportée - date à venir 
 Marine Habart (Axa)/Laurent Devineau et Alexandre Boumezoued (Milliman) Mortality data reliability in an insurance company internal model

In this paper, we discuss the impact of some mortality data anomalies on an internal model capturing longevity risk in the Solvency 2 framework. In particular, we are concerned with abnormal cohort effects such as those for generations 1919 and 1920, for which the period tables provided by the Human Mortality Database show particularly low and high mortality rates respectively. To provide corrected tables for the three countries of interest here (France, Italy and West Germany), we use the approach developed by Boumezoued (2016) for countries for which the method applies (France and Italy), and provide an extension of the method for West Germany as monthly fertility histories are not sufficient to cover the generations of interest. These mortality tables are crucial inputs to stochastic mortality models forecasting future scenarios, from which the extreme 0,5% longevity improvement can be extracted, allowing for the calculation of the Solvency Capital Requirement (SCR). More precisely, to assess the impact of such anomalies in the Solvency II framework, we use a simplified internal model based on three usual stochastic models to project mortality rates in the future combined with a closure table methodology for older ages. Correcting this bias obviously improves the data quality of the mortality inputs, which is of paramount importance today, and slightly decreases the capital requirement. Overall, the longevity risk assessment remains stable, as well as the selection of the stochastic mortality model. As a collateral gain of this data quality improvement, the more regular estimated parameters allow for new insights and a refined assessment regarding longevity risk.

Annonces Conférences
15,16,17 Janvier - Conférence de clôture de l'ARN LoLitA

Sélectionné par l’Agence Nationale de la Recherche (ANR), le projet LoLitA, porté par Nicole El Karoui (LPMA) et Stéphane Loisel (ISFA, Univ. Lyon 1) a réuni 29 chercheurs de différents laboratoires en France et à l'étranger, de décembre 2013 à Décembre 2017.

Le projet LoLitA avait pour objectif de proposer une modélisation du développement incertain de la longévité humaine à long terme, ainsi que des méthodes de gestion des risques associés à la longévité dans les domaines des retraites, de l’assurance-vie et des risques santé de long terme (dépendance).La conférence de clôture, qui se tiendra à Paris les 15, 16 et 17 janvier 2018 a pour objectif de faire le bilan des travaux menés dans le cadre du projet LoLitA. Durant 3 jours, les exposés seront présentés alternativement par les chercheurs membres du projet et 6 invited speakers internationaux.A visée prioritairement académique, la conférence est ouverte au public.

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24-25 mai - Workshop Extremes, Rare events and Machine learning
Rare and extreme events have a major impact on a wide variety of domains from environmental sciences (heat waves, flooding) to finance and insurance (financial crashes, reinsurance). Recent applications in risk management need to take complex and high dimensional data sets into account. On the other hand,  motivated by a wide variety of applications including fraud detection, monitoring of complex networks and aviation safety management, unsupervised anomaly detection has recently received much attention in the machine learning community. This important area of Machine Learning is naturally related to extreme events analysis. As an example, when a complex system is monitored by several physical variables, controlling the false alarm rate is a major issue which can be addressed in the statistical framework of extreme value theory.   The purpose of this workshop is to bring together researchers and industrials from the extreme value statistics and the machine learning communities. With a concern for applications, the workshop will include presentations with industrial applications and a round table with industrials. Topics such as random forests, anomaly detection, risk measures and extreme quantile regression will be discussed. 

Confirmed Invited Speakers: Stéphan Clémençon (Télécom ParisTech), Valérie Chavez (Université de Lausanne), Dan Cooley (Colorado State University)Anthony Davison (École Polytechnique Fédérale de Lausanne), Sebastian Engelke (Université de Genève), Stéphane Girard (Inria Grenoble Rhône-Alpes), Adrien Hitz (University of Oxford), Philippe Naveau (Laboratoire des Sciences du Climat et l'Environnement), Albert Thomas (Huawei Technologies), Jenny Wadsworth (Lancaster University), Stefan Wager (Stanford Graduate School of Business), Chen Zhou (Erasmus University Rotterdam)