Aisenstadt Chair

[ Français ]

Claudia Klüppelberg (Technische Universität München)
Stay: August 24 - September 7, 2017

Conference slideshow


Klueppelberg After studying mathematics and receiving her doctorate in 1987 at the University of Mannheim, Claudia Klüppelberg held teaching and research positions in Mannheim, at ETH Zürich and in Mainz until she was appointed Full Professor of Mathematical Statistics at the Technische Universität München in 1997. From 2008 to 2011, she also led the focus group on risk analysis and stochastic modeling at the Institute of Advanced Studies in Munich. The research interests of Professor Klüppelberg cover a large spectrum of topics in statistics and applied probability. Much of her work has been concerned with risk analysis and its applications in economics, finance, and the environment. The methods that she designed, developed, and implemented through cooperation with industry have contributed to the improvement of risk management practices. With several books and over 150 scientific articles, Professor Klüppelberg is not only a prolific author but also a co-Editor of the Springer Finance Series and the “Lévy Matters” Subseries of Springer’s Lecture Notes in Mathematics. She is an elected Fellow of the Institute of Mathematical Statistics and held various offices in the Bernoulli Society.

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

Tuesday, September 5
3:30 pm
HEC Montréal
3000, ch. de la Côte-Sainte-Catherine
1st floor
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.


Thursday, September 7

3:30 pm
Université McGill
Burnside Hall
805, Sherbrooke West.
Room 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.