Modelling Extremal Events

Volume 33 of the series Applications of Mathematics pp 21-57

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

* Final gross prices may vary according to local VAT.

Get Access


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.