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# Asymptotics of Random Contractions

## Author Info

• Enkelejd Hashorva
• Anthony G. Pakes
• Qihe Tang
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## Abstract

In this paper we discuss the asymptotic behaviour of random contractions $X=RS$, where $R$, with distribution function $F$, is a positive random variable independent of $S\in (0,1)$. Random contractions appear naturally in insurance and finance. Our principal contribution is the derivation of the tail asymptotics of $X$ assuming that $F$ is in the max-domain of attraction of an extreme value distribution and the distribution function of $S$ satisfies a regular variation property. We apply our result to derive the asymptotics of the probability of ruin for a particular discrete-time risk model. Further we quantify in our asymptotic setting the effect of the random scaling on the Conditional Tail Expectations, risk aggregation, and derive the joint asymptotic distribution of linear combinations of random contractions.

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File URL: http://arxiv.org/pdf/1008.0126

## Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1008.0126.

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 Length: Date of creation: Jul 2010 Handle: RePEc:arx:papers:1008.0126 Contact details of provider: Web page: http://arxiv.org/

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