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Subexponential tails of discounted aggregate claims in a time-dependent renewal risk model

Part of: Applications Distribution theory - Probability Multivariate analysis

Published online by Cambridge University Press:  01 July 2016

Jinzhu Li ,
Qihe Tang  and
Rong Wu
Jinzhu Li*
Affiliation:
Nankai University and The University of Iowa
Qihe Tang*
Affiliation:
The University of Iowa
Rong Wu*
Affiliation:
Nankai University
*
∗ Postal address: School of Mathematical Science and LPMC, Nankai University, Tianjin 300071, P. R. China.
∗∗∗ Postal address: Department of Statistics and Actuarial Science, The University of Iowa, 241 Schaeffer Hall, Iowa City, IA 52242, USA. Email address: qihe-tang@uiowa.edu
∗ Postal address: School of Mathematical Science and LPMC, Nankai University, Tianjin 300071, P. R. China.
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Abstract

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Consider a continuous-time renewal risk model with a constant force of interest. We assume that claim sizes and interarrival times correspondingly form a sequence of independent and identically distributed random pairs and that each pair obeys a dependence structure described via the conditional tail probability of a claim size given the interarrival time before the claim. We focus on determining the impact of this dependence structure on the asymptotic tail probability of discounted aggregate claims. Assuming that the claim size distribution is subexponential, we derive an exact locally uniform asymptotic formula, which quantitatively captures the impact of the dependence structure. When the claim size distribution is extended regularly varying tailed, we show that this asymptotic formula is globally uniform.

Keywords

Asymptoticsdependencediscounted aggregate claimextended regular variationsubexponentialityuniformity

MSC classification

Primary: 62P05: Applications to actuarial sciences and financial mathematics
Secondary: 62H20: Measures of association (correlation, canonical correlation, etc.) 60E05: Distributions
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 42 , Issue 4 , December 2010 , pp. 1126 - 1146
Copyright
Copyright © Applied Probability Trust 2010 

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