Heavy-tailed modelling in insurance

We give a short review of models appropriate for mathematically describing large insurance claims. These include typical large claims distributions, the total claim amount and the ruin probability under a large claim regime, and some problems related to reinsurance

[1]  J. Grandell.  Mixed Poisson Processes , 1997 .

[2]  Thomas Mikosch,et al.  Large Deviations of Heavy-Tailed Sums with Applications in Insurance , 1998 .

[3]  Claudia Klüppelberg,et al.  Explosive Poisson shot noise processes with applications to risk reserves , 1995 .

[4]  S. V. Nagaev,et al.  Large Deviations of Sums of Independent Random Variables , 1979 .

[5]  Claudia Klüppelberg,et al.  Delay in claim settlement and ruin probability approximations , 1995 .

[6]  Harry H. Panjer,et al.  Insurance Risk Models , 1992 .

[7]  J. Grandell.  Aspects of Risk Theory , 1991 .

[8]  Nader Tajvidi,et al.  Extreme value statistics and wind storm losses: a case study. , 1997 .

[9]  Claudia Klüppelberg,et al.  Large deviations results for subexponential tails, with applications to insurance risk , 1996 .

[10]  B. Gnedenko,et al.  Random Summation: Limit Theorems and Applications , 1996 .

[11]  P. Embrechts,et al.  Estimates for the probability of ruin with special emphasis on the possibility of large claims , 1982 .

[12]  Claudia Klüppelberg,et al.  LARGE DEVIATIONS OF HEAVY-TAILED RANDOM SUMS WITH APPLICATIONS IN INSURANCE AND FINANCE , 1997 .

[13]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[14]  C. Klüppelberg,et al.  Modelling Extremal Events , 1997 .

[15]  C. Klüppelberg,et al.  Subexponential distributions , 1998 .

[16]  A. Gut.  Stopped Random Walks , 1987 .

[17]  H. Geman,et al.  Pricing Catastrophe Insurance Futures and Call Spreads , 1995 .

[18]  J. Cummins,et al.  An Asian Option Approach to the Valuation of Insurance Futures Contracts , 1998 .

[19]  Marcin Kotulski,et al.  Asymptotic distributions of continuous-time random walks: A probabilistic approach , 1995 .

[20]  A. Nagaev.  Integral Limit Theorems Taking Large Deviations Into Account When Cramér’s Condition Does Not Hold. II , 1969 .

[21]  PAUL EMBRECHTS,et al.  Modelling of extremal events in insurance and finance , 1994, Math. Methods Oper. Res..

[22]  Harald Cram'er,et al.  Sur un nouveau théorème-limite de la théorie des probabilités , 2018 .

[23]  L. Rozovskii.  Probabilities of large deviations on the whole axis , 1994 .

[24]  J. Teugels,et al.  Practical Analysis of Extreme Values , 1996 .

[25]  J. Pickands.  Statistical Inference Using Extreme Order Statistics , 1975 .