Tails of random sums of a heavy-tailed number of light-tailed terms

Insurance: Mathematics and Economics

Volumn 43, Issue 1, 2008, Pages 85-92

  Robert, Christian Y ^a   Segers, Johan ^b  

^a Ecole Nationale de la Statistique et de l'Administration Economique   (France)

^b UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

Collective risk model; Compound distribution; Consistent variation; Heavy tailed distributions; Large deviations; Light tailed distributions; Random sum

Indexed keywords

EID: 47249113509     PISSN: 01676687     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.insmatheco.2007.10.001     Document Type: Article

References (23)

1. Anderson C.W. Local limit theorems for the maxima of discrete random variables. Mathematical Proceedings of the Cambridge Philosophical Society 88 (1980) 161-166
2. Asmussen S., Klüppelberg C., and Sigman K. Sampling at subexponential times, with queueing applications. Stochastic Processes and their Applications 79 (1999) 265-286
3. Baltrunas A., Daley D.J., and Klüppelberg C. Tail behaviour of the busy period of a G I / G / 1 queue with subexponential service times. Stochastic Processes and their Applications 111 (2004) 237-258
4. Beard R., Pentikainen R., and Pesonen E. Risk Theory (1984), Chapman & Hall, Boca Raton
5. Bingham N.C., Goldie C.M., and Teugels J.L. Regular Variation (1987), Cambridge University Press, Cambridge
6. Cai J., and Tang Q. On max-sum equivalence and convolution closure of heavy-tailed distributions and their applications. Journal of Applied Probability 41 1 (2004) 117-130
7. Cline D.B.H. Intermediate regular and Π variation. Proceedings of the London Mathematical Society 68 3 (1994) 594-616 Third series
8. Cline D.B.H., and Samorodnitsky G. Subexponentiality of the product of independent random variables. Stochastic Processes and their Applications 49 (1994) 75-98
9. Denisov, D., Foss, S., Korshunov, D., 2007. On lower limits and equivalences for distribution tails of randomly stopped sums. EURANDOM Report 2007-004, http://www.eurandom.nl/
10. Embrechts P., Klüppelberg C., and Mikosch T. Modelling Extremal Events for Finance and Insurance (1997), Springer-Verlag, Berlin
11. Fay G., Gonzalez-Arevalo B., Mikosch T., and Samorodnitsky G. Modeling teletraffic arrivals by a Poisson cluster process. Queueing Systems 54 2 (2006) 121-140
12. Feller W. An Introduction to Probability Theory and its Applications vol. II (1971), John Wiley & Sons, New York
13. Foss S., and Korshunov D.A. Sampling at a random time with a heavy-tailed distribution. Markov Processes and Related Fields 6 (2000) 643-658
14. Gutenberg R., and Richter C.F. Frequency of earthquakes in California. Bulletin of the Seismological Society of America 34 (1944) 185-188
15. Jensen J.L. Saddlepoint Approximations (1995), Oxford University Press
16. Kaas R., Goovaerts M., Dhaene J., and Denuit M. Modern Actuarial Risk Theory (2001), Kluwer Academic Publishers, Boston
17. Kaas R., and Tang Q. A large deviations result for aggregate claims with dependent claim occurrences. Insurance: Mathematics and Economics 36 3 (2005) 251-259
18. Ng K.W., Tang Q., Yan J., and Yang H. Precise large deviations for sums of random variables with consistently varying tails. Journal of Applied Probability 41 1 (2004) 93-107
19. Resnick S., and Samorodnitsky G. Performance decay in a single server exponential queueing model with long-range dependence. Operations Research 45 2 (1997) 235-243
20. Schmidli H. Compound sums and subexponentiality. Bernoulli 5 (1999) 999-1012
21. Stam A.J. Regular variation of the tail of a subordinated distribution. Advances in Applied Probability 5 (1973) 308-327
22. Tang Q. Asymptotics for the finite time ruin probability in the renewal model with consistent variation. Stochastic Models 20 3 (2004) 281-297
23. Tang Q. Insensitivity to negative dependence of the asymptotic behavior of precise large deviations. Electronic Journal of Probability 11 (2006) 107-120