Heavy-tailed modelling in insurance

References

• Aase , K. 1994 . An equilibrium model of catastrophic insurance futures contracts . Preprint ,
   Google Scholar
• Asmussen , S. 1996 . Ruin Probabilities . World Scientific ,
   Google Scholar
• Asmussen , S. and Kliippelberg , C. 1996 . Large deviation results for subex-ponential tails, with applications to insurance risk . Stock. Proc. Appl. , 64 : 103 – 127 .
   Web of Science ®Google Scholar
• Beirlant , J. , Teugels , J. L. and Vynckier , P. 1996 . “ Practical Analysis of Extreme Values ” . Leuven : Leuven University Press .
   Google Scholar
• 1995a . The Chicago Board of Trade, Catastrophe Insurance . Background Report ,
   Google Scholar
• 1995b . The Chicago Board of Trade, Catastrophe Insurance . Reference Guide ,
   Google Scholar
• 1995c . The Chicago Board of Trade, PCS Options . A User's Guide ,
   Google Scholar
• Cramer , H. 1938 . Sur un nouveau theoreme-limite de la theorie des probability . Actualites Sci. Indust. , : 736
   Google Scholar
• Cummins , J. D. and Geman , H. 1994 . An Asian option approach to the valuation of insurance futures contracts . Review Futures Markets , 13 : 517 – 557 .
   Google Scholar
• Cummins , J. D. and Geman , H. 1995 . Pricing catastrophe futures and call spreads: an arbitrage approach . Journal of Fixed Income , 4 : 46 – 57 .
   Google Scholar
• Embrechts , P. , Kluppelberg , C. and Mikosch , T. 1997 . “ Modelling Extremal Events for Insurance and Finance ” . Springer, Berlin . to appear
   Google Scholar
• Embrechts , P. and Veraverbeke , N. 1982 . Estimates for the probability of ruin with special emphasis on the possibility of large claims . Insurance: Math. Econom. , 1 : 55 – 72 .
   Web of Science ®Google Scholar
• Feller , W. 1971 . “ An Introduction to Probability Theory and Its Applications II ” . New York : Wiley .
   Google Scholar
• Gnedenko , B. V. and Korolev , V. Yu. 1996 . “ Random Summation ” . Boca Raton : CRC Press .
   Google Scholar
• Goldie , C. M. and Kluppelberg , C. 1997 . “ Subexponential distributions ” . In A Practical Guide to Heavy Tails: Statistical Techniques for Analysing Heavy-Tailed Distributions Edited by: Adler , R. , Feldman , R. and Taqqu , M. S. Birkhauser, Boston
   Google Scholar
• Grandell , J. 1991 . “ Aspects of Risk Theory ” . Berlin : Springer .
   Google Scholar
• Grandell , J. 1997 . “ Mixed Poisson Processes ” . London : Chapman and Hall .
   Google Scholar
• Gut , A. 1988 . “ Stopped Random Walk ” . In Limit Theorems and Applications , New York : Springer .
   Google Scholar
• Hogg , R. V. and Klugman , S. A. 1984 . “ Loss Distributions ” . New York : Wiley .
   Google Scholar
• Kluppelberg , C. and Mikosch , T. 1995a . Explosive shot noise processes with applications to risk retention . Bernoulli , 1 : 125 – 147 .
   Google Scholar
• Kluppelberg , C. and Mikosch , T. 1995b . Modelling delay in claim settlement . Scand. Actuar. J. , 1 : 154 – 168 .
   Google Scholar
• Kluppelberg , C. and Mikosch , T. 1997 . Large deviations of heavy-tailed random sums with applications to insurance and finance . J. Appl. Probab. , 34
   Google Scholar
• Kotulski , M. 1995 . Asymptotic distributions of the continuous-time random walks: a probabilistic approach . J. Statist. Phys. , 81 : 777 – 792 .
   Google Scholar
• Meister , S. 1995 . “ Contributions to the Mathematics of Catastrophe Insurance Futures ETH Zurich ” . Diplomarbeit .
   Google Scholar
• Mikosch , T. and Nagaev , A. V. 1997 . “ Large deviations for heavy-tailed sums with applications in insurance ” . Preprint
   Google Scholar
• Nagaev , A. V. 1969a . Limit theorems for large deviations where Cramer's conditions are violated . Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat. Nauk , 6 : 17 – 22 . in Russian
   Google Scholar
• Nagaev , A. V. 1969b . Integral limit theorems for large deviations when Cramer's condition is not fulfilled I,II . Theory Probab. Appl. , 14 : 193 – 208 .
   Web of Science ®Google Scholar
• Nagaev , S. V. 1979 . Large deviations of sums of independent random variables . Ann. Probab. , 7 : 745 – 789 .
   Web of Science ®Google Scholar
• Panjer , H. H. and Willmot , G. 1992 . “ Insurance Risk Models ” . Schaumburg, Illinois : Society of Actuaries .
   Google Scholar
• Pickands , J. 1975 . Statistical inference using extreme order statistics . Ann. Statist. , 3 : 119 – 131 .
   Web of Science ®Google Scholar
• Rootzen , H. and Tajvidi , N. 1997 . Extreme value statistics and wind storm losses: a case study . Scand. Actuar. J , 3
   Google Scholar
• Rozovski , L. V. 1994 . Probabilities of large deviations on the whole axis . Theory Probab. Appl. , 38 : 53 – 79 .
   Google Scholar
• Schradin , H. D. and Moller , M. 1996 . Einsatz von Optionen auf den PCS-Schadenindex in der Risikosteuerung von Versicherungsunternehmen. Manuskript No 88 . Inst. f. Versicherungswissenschaft, Universitat Mannheim , 38
   Google Scholar
• 1996 . Non-proportional reinsurance of losses due to natural disasters in 1995: Prices down despite insufficient cover . Sigma publication No 6, Swiss Re, Zurich , 38
   Google Scholar
• 1996 . Insurance derivatives and securitization: New hedging perspectives for the US catastrophe insurance market . Sigma publication No 5, Swiss Re, Zurich , 38
   Google Scholar
• Smith , R. L. 1990 . “ Extreme value theory ” . In Handbook of Applicable Mathematics, Supplement , Edited by: Ledermann , W. 437 – 472 . Chichester : Wiley .
   Google Scholar