We study boundary crossings for single and multivariate components of a compound Poisson process. The dependence structure between the components is induced by a random bipartite graph. The focus of our analysis lies in the study of the influence of the random graph on boundary crossings, where we consider the Bernoulli graph and a Rasch-type graph as examples. We investigate the influence of the random graph on subsets of components. In particular, we contrast the influence of the network on single components and on multivariate vectors. As applications, risk balancing networks in ruin theory and load balancing networks in queueing theory are presented. This is the joint work with Anita Behme and Gesine Reinert.
Claudia Klüppelberg is a full Professor for Mathematical Statistics at the Technical University of Munich. After studying mathematics and receiving her doctorate (1987) at the University of Mannheim, she completed her Habilitation at ETH Zurich (1993). Her research interests lies in probabilistic risk modelling and the development of new methods for risk assessment. At present her work focuses on risk spreading in networks. Along with more than 150 publications in scientific journals, she has edited various books, and written the book “Modelling Extremal Events for Insurance and Finance (jointly with Paul Embrechts and Thomas Mikosch). She is an Elected Fellow of the Institute of Mathematical Statistics and President Elect of the Bernoulli Society.
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