Volume 33 of the series Applications of Mathematics pp 2157
Risk Theory
 Paul EmberchtsAffiliated withDepartment of Mathematics, ETH Zurich
 , Claudia KlüppelbergAffiliated withCenter for Mathematical Sciences, Munich University of Technology
 , Thomas MikoschAffiliated withLaboratory of Actuarial Mathematics, University of Copenhagen
Abstract
For most of the problems treated in insurance mathematics, risk theory still provides the quintessential mathematical basis. The present chapter will serve a similar purpose for the rest of this book. The basic risk theory models will be introduced, stressing the instances where a division between small and large claims is relevant. Nowadays, there is a multitude of textbooks available treating risk theory at various mathematical levels. Consequently, our treatment will not be encyclopaedic, but will focus more on those aspects of the theory where we feel that, for modelling extremal events, the existing literature needs complementing. Readers with a background in finance rather than insurance may use this chapter as a first introduction to the stochastic modelling of claim processes.
 Title
 Risk Theory
 Book Title
 Modelling Extremal Events
 Book Subtitle
 for Insurance and Finance
 Pages
 pp 2157
 Copyright
 1997
 DOI
 10.1007/9783642334832_2
 Print ISBN
 9783642082429
 Online ISBN
 9783642334832
 Series Title
 Applications of Mathematics
 Series Volume
 33
 Series Subtitle
 Stochastic Modelling and Applied Probability
 Series ISSN
 01724568
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
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 Authors

 Paul Emberchts ^{(6)}
 Claudia Klüppelberg ^{(7)}
 Thomas Mikosch ^{(8)}
 Author Affiliations

 6. Department of Mathematics, ETH Zurich, 8092, Zurich, Switzerland
 7. Center for Mathematical Sciences, Munich University of Technology, Boltzmannstraße 3, 85747, Garching, Germany
 8. Laboratory of Actuarial Mathematics, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen, Denmark
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