Chaire Aisenstadt

[ English ]

Claudia Klüppelberg (Technische Universität München)
Séjour: 24 août - 7 septembre 2017

Diaporama de la conférence

Video

Kluppelberg Après avoir étudié les mathématiques et soutenu sa thèse en 1987 à l'Université de Mannheim, Claudia Klüppelberg a occupé des postes d'enseignement et de recherche à Mannheim, ETH Zürich et Mainz avant d’être nommée titulaire de la chaire de statistique mathématique à la Technische Universität München en 1997. De 2008 à 2011, elle a aussi dirigé un groupe de recherche sur les modèles stochastiques et l'analyse du risque à l'Institut des études avancées de Munich. Les intérêts de recherche du professeur Klüppelberg couvrent un large éventail de sujets en statistique et en probabilités appliquées. Ses travaux portent en grande partie sur l'analyse du risque et ses applications en économique, en finance et dans le secteur de l'environnement. Les nombreuses méthodes qu'elle a conçues, développées et mises en pratique au fil de collaborations avec l'industrie ont permis d'améliorer la gestion du risque. Auteur prolifique qui a à son actif plus de 150 publications et ouvrages scientifiques, le professeur Klüppelberg codirige la collection Springer Finance, ainsi que la série « Lévy Matters » des Lecture Notes in Mathematics chez le même éditeur. Elle est compagnon de l'Institut de statistique mathématique et a exercé diverses fonctions au sein de la Société Bernoulli.

Jeudi 24 août / Thursday, August 24
15h30 / 3:30 pm

Conférence s'adressant à un large auditoire scientifique
Lecture suitable for a general scientific audience

Centre de recherches mathématiques
Pavillon André-Aisenstadt
Université de Montréal
Salle / Room 6214

"Risk and conditional risk measures in an agent-object insurance market"
[ Diapos de la conférence / Conference slides ]

We introduce a random network model for business relationships exemplified for a re-insurance market. Using Pareto-tailed losses (as are observed for natural or man-made catastrophes) with a dependence structure introduced by the graph we study systemic risk measures, which are based on the Value-at-Risk and the Expected Shortfall. We show that the dependence on the network structure plays a fundamental role for the individual agent’s risk as well as for the systemic risk. If the Pareto exponent is larger than 1, then for the individual agent diversification is beneficial, whereas when it is less than one, concentration on a few objects is the better strategy for individual agents. The situation changes, however, when systemic risk comes into play. We describe different network scenarios including a homogeneous model and a Rasch-type model, and explain the influence of the network structure on diversification in such models. This is joint work with Oliver Kley and Gesine Reinert and the first paper received the Lloyd’s Science of Risk Price in 2016.

[1] Kley, O., Klüppelberg, C., and Reinert G.: Risk in a large claims insurance market with bipartite graph structure. Operations Research 64 (5), 2016, 1159-1176.
[2] Kley, O., Klüppelberg, C., and Reinert, G.: Conditional risk measures in a bipartite market structure. Scandinavian Actuarial Journal, Published online http://dx.doi.org/10.1080/03461238.2017.1350203

Mardi 5 septembre
15h30
HEC Montréal
3000, chemin de la Côte-Sainte-Catherine, 1er étage
Salle Room Transat

"Semiparametric estimation of space-time extremes"

Max-stable space-time processes have been developed to study extremal dependence in space-time data. We propose a semiparametric estimation procedure based on a closed form expression of the extremogram to estimate the parameters in a max-stable space-time process. We establish the asymptotic properties of the resulting parameter estimates based on a CLT for the empirical extremogram. We also propose subsampling procedures to obtain asymptotically correct confidence intervals. A simulation study shows that the proposed procedure works well for moderate sample sizes. Finally, we apply this estimation procedure to fitting a max-stable model to radar rainfall measurements in a region in Florida.

This is joint work with Sven Buhl, Richard Davis, and Christina Steinkohl.
[1] Buhl, S., Davis, R.A., Klüppelberg, C. and Steinkohl, C. (2016) Semiparametric estimation for isotropic max-stable space-time processes. Under revision.
[2] Buhl, S. and Klüppelberg, C. (2016) Limit theory for the empirical extremogram of random fields. Under revision.

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Jeudi 7 septembre
15h30
Université McGill
Burnside Hall
805, rue Sherbrooke Ouest
Salle 1205

"Can we identify a max-linear model on a directed acyclic graph by the tail correlation matrix?"

We investigate multivariate regularly varying random vectors with discrete spectral measure induced by a directed acyclic graph (DAG). The tail dependence coefficient measures extreme dependence between two vector components, and we investigate how the matrix of tail dependence coefficients can be used to identify the full dependence structure of the random vector on a DAG or even the DAG itself. Furthermore, we estimate the distributional model by the matrix of empirical tail dependence coefficients. From these observations we want to infer the causal dependence structure in the data. This is joint work with Nadine Gissibl and Moritz Otto.

[1] Gissibl, N. and Klüppelberg, C. (2015) Max-linear models on directed acyclic graphs. Under revision.
[2] Gissibl, N., Klüppelberg, C. and Otto, M. (2017)
Tail dependence of recursive max-linear models with regularly varying noise variables. Submitted.