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References (10)
-
Tang (2004)
Asymptotics for the finite time ruin probability in the renewal model with consistent variationStochastic Models, 20
-
Leipus (2007)
Asymptotic behaviour of the finite-time ruin probability under subexponential claim sizesInsurance: Mathematics and Economics, 40
-
Korshunov Korshunov (2002)
Large‐deviation probabilities for maxima of sums of independent random variables with negative mean and subexponential distributionTheory of Probability and Its Applications, 46
-
Sgibnev Sgibnev (1997)
Submultiplicative moments of the supremum of a random walk with negative driftStatistics and Probability Letters, 32
-
Kaas Kaas, Tang Tang (2003)
Note on the tail behavior of random walk maxima with heavy tails and negative driftNorth American Actuarial Journal, 7
-
Asmussen (1984)
Approximations for the probability of ruin within finite timeScandinavian Actuarial Journal, 1
-
Pitman Pitman (1980)
Subexponential distribution functionsJournal of Australian Mathematical Society, Series A, 29
-
Klüppelberg Klüppelberg, Mikosch Mikosch (1997)
Large deviations of heavy‐tailed random sums with applications in insurance and financeJournal of Applied Probability, 34
-
Embrechts (1982)
Estimates for the probability of ruin with special emphasis on the possibility of large claimsInsurance: Mathematics and Economics, 1
-
Baltrūnas Baltrūnas, Leipus Leipus, Šiaulys Šiaulys (2008)
Precise large deviation results for the total claim amount under subexponential claim sizesStatistics and Probability Letters, 78
- Publisher
- Wiley
- Copyright
- Copyright © 2008 John Wiley & Sons, Ltd.
- ISSN
- 1524-1904
- eISSN
- 1526-4025
- DOI
- 10.1002/asmb.747
- Publisher site
- See Article on Publisher Site
Abstract
In this paper we study the tail behaviour of the probability of ruin within finite time t, as initial risk reserve x tends to infinity, for the renewal risk model with strongly subexponential claim sizes. The asymptotic formula holds uniformly for t∈(f(x), ∞), where f(x) is an infinitely increasing function, and substantially extends the result of Tang (Stoch. Models 2004; 20:281–297) obtained for the class of claim distributions with consistently varying tails. Two examples illustrate the result. Copyright © 2008 John Wiley & Sons, Ltd.
Journal
Applied Stochastic Models in Business and Industry – Wiley
Published: May 1, 2009