On the number of near-maximum insurance claim under dependence

Details

Serval ID
serval:BIB_861731129415
Type
Article: article from journal or magazin.
Collection
Publications
Title
On the number of near-maximum insurance claim under dependence
Journal
Insurance: Mathematics and Economics
Author(s)
Hashorva E.
ISSN
0167-6687
Publication state
Published
Issued date
2003
Peer-reviewed
Oui
Volume
32
Number
1
Pages
37-49
Language
english
Abstract
Let X-1, X-2,... be random claim sizes with continuous distribution functions F and N((.)) an independent point process on [0, infinity). Denote by X-N([0,X-t):N([0,X-t) the maximal claim size occurring during the time interval [0,t], t>0 and K-t (a) the number of claims that excess the random barrier XN([0,t])-a(t), with a(t)>0. For iid claim sizes, both distributional and asymptotic properties of K-t (a) are investigated in Li and Pakes (2001) [Li, Y, Pakes, A.G., Insur.: Math. Econ. 28 (3), 309-323]. In this paper, by dropping the iid assumption we extend and simplify limit results of Li and Pakes (2001). Further, we show that K-t (a)/t is a strongly consistent estimator of certain tail probability.
Keywords
Near-maximum insurance claim, Extreme value theory, Stationary random sequence, Limit results
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Create date
03/09/2010 11:16
Last modification date
20/08/2019 14:45
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