Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/103618
Authors: 
Albrecher, Hansjörg
Robert, Christian Yann
Teugels, Jezef L.
Year of Publication: 
2014
Citation: 
[Journal:] Risks [ISSN:] 2227-9091 [Publisher:] MDPI [Place:] Basel [Volume:] 2 [Year:] 2014 [Issue:] 3 [Pages:] 289-314
Abstract: 
Assume that claims in a portfolio of insurance contracts are described by independent and identically distributed random variables with regularly varying tails and occur according to a near mixed Poisson process. We provide a collection of results pertaining to the joint asymptotic Laplace transforms of the normalised sums of the smallest and largest claims, when the length of the considered time interval tends to infinity. The results crucially depend on the value of the tail index of the claim distribution, as well as on the number of largest claims under consideration.
Subjects: 
aggregate claims
ammeter problem
near mixed Poisson process
reinsurance
subexponential distributions
extremes
Persistent Identifier of the first edition: 
Creative Commons License: 
http://creativecommons.org/licenses/by/3.0/
Document Type: 
Article
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