We provide a new extension of Breiman’s Theorem on computing tail probabilities of a product of random variables to a multivariate setting. In particular, we give a complete characterisation of regular variation on cones in [0, ∞)d under random linear transformations. This allows us to compute probabilities of a variety of tail events, which classical multivariate regularly varying models would report to be asymptotically negligible. We present relevant applications to risk assessment in insurance markets under a bipartite network structure. This is the joint work with Bikramjit Das and Vicky Fasen-Hartmann.
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 of the Bernoulli Society.
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