Risk Theory
 Paul Emberchts,
 Claudia Klüppelberg,
 Thomas Mikosch
 … show all 3 hide
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.
 Veraverbeke, N. (1993) Asymptotic estimates for the probability of ruin in a Poisson model with diffusion. Insurance: Math. Econom. 13, 57–62. [56]
 Furrer, H.J. and Schmidli, H. (1994) Exponential inequalities for ruin probabilities of risk processes perturbed by diffusion. Insurance: Math. Econom.15, 23–36. [56]
 Asmussen, S., Floe Henriksen, L. and Klüppelberg, C. (1994) Large claims approximations for risk processes in a Markovian environment. Stoch. Proc. Appl. 54, 29–43. [56, 454]
 Reinhard, J.M. (1984) On a class of semiMarkov risk models obtained as classical risk models in a Markovian environment. ASTIN Bulletin 14, 2343. [57]
 Klüppelberg, C. and Stadtmüller, U. (1998) Ruin probabilities in the presence of heavytails and interest rates. Scand. Actuar. J., 49–58. [57]
 Asmussen, S. (1998) Subexponential asymptotics for stochastic processes: extremal behaviour, stationary distributions and first passage probabilities. Ann. Appl. Probab. 8, 354–374. [57]
 Embrechts, P. (1983) A property of the generalized inverse Gaussian distribution with some applications. J. Appl. Probab. 20, 537–544. [36, 57]
 Omey, E. and Willekens, E. (1986) Second order behaviour of the tail of a subordinated probability distribution. Stoch. Proc. Appl. 21, 339–353. [57]
 Omey, E. and Willekens, E. (1987) Second order behaviour of distributions subordinate to a distribution with finite mean. Commun. Statist. Stochastic Models 3, 311–342. [57]
 Asmussen, S. and Binswanger, K. (1997) Simulation of ruin probabilities for subexponential claims. ASTIN Bulletin 27, 297–318. [57, 454]
 Binswanger, K. (1997) Rare Events in Insurance. PhD thesis, ETH Zürich. [57]
 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
 Additional Links
 Topics
 Industry Sectors
 eBook Packages
 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
Continue reading...
To view the rest of this content please follow the download PDF link above.