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)
Couloir 16-26 Salle 113 (1er étage) 

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

Prochaines séances 

** Séance exceptionnelle - Jeudi 14 Décembre à 10h15 - salle 16-26 116**
Ana Debon (Universidad Politécnica de Valencia) - Spatial Statistical Tools to Assess Mortality Differences in Europe
In general, life expectancy has increased in the whole of Europe in recent decades, especially in western European countries. However, this study detected that the observed mortality is higher than expected in eastern European countries, widening the gap between these countries and Western Europe. The main objective of this paper is to study the space dependence of significant clusters through a spatial panel data model. There are many studies that address the decrease of mortality in Europe. None of them uses spatial methodology to detect significant clusters between countries with similar mortality, implementing in turn a spatial model which controls the space dependence of the European countries over time. 
Thus, the objective of this study is to determine differentiated behavior areas and control the spatial interaction between European countries over time applying a spatial panel data model.The methodology takes into account the neighboring relationships between the countries. The performance of the model was assessed using the methods of goodness of fit, residual variance, and determination coefficient. This statistical methodology was applied to 26 European countries over the period 1990–2009. The R free software environment for statistical computing was used to perform 

Vendredi 15 décembre 
** Séance d'1h30**
Simone Padoan (Univestità Bocconi di Milano, Italie) Nonparametric Estimation of the Pickands Dependence Function:

Asymptotic Dependence and Independence Cases

Many applications in risk analysis require the estimation of the dependence among multivariate maxima, especially in environmental sciences. Such dependence can be

described by the Pickands dependence function of the underlying extreme-value copula. A nonparametric estimator is constructed as the sample equivalent of a multivariate

extension of the madogram. We discuss the The large-sample theory of the estimator and  we show its finite-sample performance with a simulation study.

We also describe a statistical test based on the Pickands dependence function to verify whether asymptotic dependence or independence holds. Then, we introduce a Pickands dependence function to describe the extremal dependence under asymptotic independence and we propose an estimator of it. 

We discuss its main asymptotic properties and its performance is illustrated by a simulation study.

Rafal Kulik (University of Ottawa, Canada) -  Limit theorems for empirical cluster functionals with application to statistical inference
 Limit theorems for empirical cluster functionals are discussed. Conditions for weak convergence are provided in terms of tail and spectral tail processes and can be verified for a large class of multivariate time series, including geometrically ergodic Markov chains. Applications include asymptotic normality of blocks and runs estimators for the extremal index and other cluster indices. Results for multiplier bootstrap processes are also provided.

Vendredi 26 janvier 
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 19 Janvier
** Séance d'1h30 - !! Attention salle 15-16 101 !! **
Thomas Mikosch (University of Copenhagen, Danemark) - TBA
Hrovje Planinic (University of Zagreb, Croatie) -  TBA
Jean-Marc Bardet (Université Paris Sorbonne) - TBA

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

Vendredi 16 Février 
 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.

Vendredi 9 Mars
Johannes Heiny (Aarhus University) - TBA