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Heavy tails of discounted aggregate claims in the continuous-time renewal model
Qihe Tang
Source: J. Appl. Probab. Volume 44, Number 2 (2007), 285-294.
Abstract
We study the tail behavior of discounted aggregate claims in a continuous-time renewal model. For the case of Pareto-type claims, we establish a tail asymptotic formula, which holds uniformly in time.
Primary Subjects: 91B30
Secondary Subjects: 60G55, 60G70
Keywords: Asymptotics; extended regular variation; renewal process; uniformity
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jap/1183667401
Digital Object Identifier: doi:10.1239/jap/1183667401
Mathematical Reviews number (MathSciNet):
MR2340198
Zentralblatt MATH identifier:
05238121
References
Asmussen, S. (2003). Applied Probability and Queues. 2nd edn. Springer, New York.
Mathematical Reviews (MathSciNet):
MR1978607
Zentralblatt MATH:
1029.60001
Bingham, N. H., Goldie, C. M. and Teugels, J. L. (1987). Regular variation. Cambridge University Press.
Mathematical Reviews (MathSciNet):
MR898871
Zentralblatt MATH:
0617.26001
Chen, Y. and Ng, K. W. (2007). The ruin probability of the renewal model with constant interest force and negatively dependent heavy-tailed claims. Insurance Math. Econom. 40, 415--423.
Mathematical Reviews (MathSciNet):
MR2310980
Embrechts, P., Klüppelberg, C. and Mikosch, T. (1997). Modelling Extremal Events for Insurance and Finance. Springer, Berlin.
Mathematical Reviews (MathSciNet):
MR1458613
Zentralblatt MATH:
0873.62116
Goldie, C. M. (1978). Subexponential distributions and dominated-variation tails. J. Appl. Prob. 15, 440--442.
Mathematical Reviews (MathSciNet):
MR474459
Digital Object Identifier: doi:10.2307/3213416
JSTOR: links.jstor.org
Klüppelberg, C. and Mikosch, T. (1997). Large deviations of heavy-tailed random sums with applications in insurance and finance. J. Appl. Prob. 34, 293--308.
Mathematical Reviews (MathSciNet):
MR1447336
Digital Object Identifier: doi:10.2307/3215371
JSTOR: links.jstor.org
Klüppelberg, C. and Stadtmüller, U. (1998). Ruin probabilities in the presence of heavy-tails and interest rates. Scand. Actuarial J. 1998, 49--58.
Mathematical Reviews (MathSciNet):
MR1626664
Nagaev, S. V. (1979). Large deviations of sums of independent random variables. Ann. Prob. 7, 745--789.
Mathematical Reviews (MathSciNet):
MR542129
Digital Object Identifier: doi:10.1214/aop/1176994938
Project Euclid: euclid.aop/1176994938
Tang, Q. (2004). Uniform estimates for the tail probability of maxima over finite horizons with subexponential tails. Prob. Eng. Inf. Sci. 18, 71--86.
Mathematical Reviews (MathSciNet):
MR2023389
Digital Object Identifier: doi:10.1017/S0269964804181059
Tang, Q. (2005). The finite-time ruin probability of the compound Poisson model with constant interest force. J. Appl. Prob. 42, 608--619.
Mathematical Reviews (MathSciNet):
MR2157508
Digital Object Identifier: doi:10.1239/jap/1127322015
Project Euclid: euclid.jap/1127322015
Tang, Q. and Tsitsiashvili, G. (2003). Randomly weighted sums of subexponential random variables with application to ruin theory. Extremes 6, 171--188.
Mathematical Reviews (MathSciNet):
MR2081850
Digital Object Identifier: doi:10.1023/B:EXTR.0000031178.19509.57
Tang, Q. and Tsitsiashvili, G. (2004). Finite- and infinite-time ruin probabilities in the presence of stochastic returns on investments. Adv. Appl. Prob. 36, 1278--1299.
Mathematical Reviews (MathSciNet):
MR2119864
Digital Object Identifier: doi:10.1239/aap/1103662967
Project Euclid: euclid.aap/1103662967
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