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

  • Qihe Tang (a1)

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.

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Copyright

Corresponding author

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

References

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[1] Asmussen, S. (2003). Applied Probability and Queues. 2nd edn. Springer, New York.
[2] Bingham, N. H., Goldie, C. M. and Teugels, J. L. (1987). Regular variation. Cambridge University Press.
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[8] Nagaev, S. V. (1979). Large deviations of sums of independent random variables. Ann. Prob. 7, 745789.
[9] Tang, Q. (2004). Uniform estimates for the tail probability of maxima over finite horizons with subexponential tails. Prob. Eng. Inf. Sci. 18, 7186.
[10] Tang, Q. (2005). The finite-time ruin probability of the compound Poisson model with constant interest force. J. Appl. Prob. 42, 608619.
[11] Tang, Q. and Tsitsiashvili, G. (2003). Randomly weighted sums of subexponential random variables with application to ruin theory. Extremes 6, 171188.
[12] Tang, Q. and Tsitsiashvili, G. (2004). Finite- and infinite-time ruin probabilities in the presence of stochastic returns on investments. Adv. Appl. Prob. 36, 12781299.

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

  • Qihe Tang (a1)

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