Skip to main content

Precise large deviations for the prospective-loss process

  • Kai W. Ng (a1), Qihe Tang (a2), Jiaan Yan (a3) and Hailiang Yang (a1)

In this paper, we propose a customer-arrival-based insurance risk model, in which customers' potential claims are described as independent and identically distributed heavy-tailed random variables and premiums are the same for each policy. We obtain some precise large deviation results for the prospective-loss process under a mild assumption on the random index (in our case, the customer-arrival process), which is much weaker than that in the literature.

Corresponding author
Postal address: Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong.
∗∗ Postal address: Department of Quantitative Economics, University of Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, The Netherlands.
∗∗∗ Postal address: Academy of Mathematics and System Sciences, The Chinese Academy of Sciences, Beijing 100080, P. R. China.
∗∗∗∗ Email address:
Hide All
Asmussen, S. (2000). Ruin Probabilities. World Scientific, Singapore.
Asmussen, S. and Klüppelberg, C. (1996). Large deviation results for subexponential tail, with applications to insurance risk. Stoch. Process. Appl. 64, 103125.
Bingham, N. H., Goldie, C. M., and Teugels, J. L. (1987). Regular Variation. Cambridge University Press.
Cline, D. B. H., and Hsing, T. (1991). Large deviation probabilities for sums and maxima of random variables with heavy or subexponential tails. Preprint, Texas A&M University.
Embrechts, P., Klüppelberg, C., and Mikosch, T. (1997). Modelling Extremal Events for Insurance and Finance. Springer, Berlin.
Klüppelberg, C., and Mikosch, T. (1997). Large deviations of heavy-tailed random sums with applications in insurance and finance. J. Appl. Prob. 34, 293308.
Mikosch, T., and Nagaev, A. V. (1998). Large deviations of heavy-tailed sums with applications in insurance. Extremes 1, 81110.
Rolski, T., Schmidli, H., Schmidt, V., and Teugels, J. (1999). Stochastic Processes for Insurance and Finance. John Wiley, Chichester.
Tang, Q. H., and Yan, J. A. (2002). A sharp inequality for the tail probabilities of sums of i.i.d. r.v.'s with dominatedly varying tails. Sci. China A 45, 10061011.
Tang, Q. H., Su, C., Jiang, T., and Zhang, J. S. (2001). Large deviations for heavy-tailed random sums in compound renewal model. Statist. Prob. Lett. 52, 91100.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


MSC classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed