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Heavy Tails of Discounted Aggregate Claims in the Continuous-Time Renewal Model

Part of: Stochastic processes Mathematical economics

Published online by Cambridge University Press:  14 July 2016

Qihe Tang
Qihe Tang*
Affiliation:
The University of Iowa
*
∗ Postal address: Department of Statistics and Actuarial Science, The University of Iowa, 241 Schaeffer Hall, Iowa City, IA 52242, USA. Email address: qtang@stat.uiowa.edu
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Abstract

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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.

Keywords

Asymptoticsextended regular variationrenewal processuniformity

MSC classification

Primary: 91B30: Risk theory, insurance
Secondary: 60G55: Point processes 60G70: Extreme value theory; extremal processes
Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 2 , June 2007 , pp. 285 - 294
Copyright
Copyright © Applied Probability Trust 2007 

References

Asmussen, S. (2003). Applied Probability and Queues. 2nd edn. Springer, New York.Google Scholar
Bingham, N. H., Goldie, C. M. and Teugels, J. L. (1987). Regular variation. Cambridge University Press.CrossRefGoogle Scholar
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.Google Scholar
Embrechts, P., Klüppelberg, C. and Mikosch, T. (1997). Modelling Extremal Events for Insurance and Finance. Springer, Berlin.CrossRefGoogle Scholar
Goldie, C. M. (1978). Subexponential distributions and dominated-variation tails. J. Appl. Prob. 15, 440–442.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Klüppelberg, C. and Stadtmüller, U. (1998). Ruin probabilities in the presence of heavy-tails and interest rates. Scand. Actuarial J. 1998, 49–58.CrossRefGoogle Scholar
Nagaev, S. V. (1979). Large deviations of sums of independent random variables. Ann. Prob. 7, 745–789.CrossRefGoogle Scholar
Tang, Q. (2004). Uniform estimates for the tail probability of maxima over finite horizons with subexponential tails. Prob. Eng. Inf. Sci. 18, 71–86.Google Scholar
Tang, Q. (2005). The finite-time ruin probability of the compound Poisson model with constant interest force. J. Appl. Prob. 42, 608–619.CrossRefGoogle Scholar
Tang, Q. and Tsitsiashvili, G. (2003). Randomly weighted sums of subexponential random variables with application to ruin theory. Extremes 6, 171–188.Google Scholar
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.CrossRefGoogle Scholar