Translator Disclaimer
November 2015 A new class of large claim size distributions: Definition, properties, and ruin theory
Sergej Beck, Jochen Blath, Michael Scheutzow
Bernoulli 21(4): 2457-2483 (November 2015). DOI: 10.3150/14-BEJ651

Abstract

We investigate a new natural class $\mathcal{J}$ of probability distributions modeling large claim sizes, motivated by the ‘principle of one big jump’. Though significantly more general than the (sub-)class of subexponential distributions $\mathcal{S}$, many important and desirable structural properties can still be derived. We establish relations to many other important large claim distribution classes (such as $\mathcal{D}$, $\mathcal{S}$, $\mathcal{L}$, $\mathcal{K}$, $\mathcal{OS}$ and $\mathcal{OL}$), discuss the stability of $\mathcal{J}$ under tail-equivalence, convolution, convolution roots, random sums and mixture, and then apply these results to derive a partial analogue of the famous Pakes–Veraverbeke–Embrechts theorem from ruin theory for $\mathcal{J}$. Finally, we discuss the (weak) tail-equivalence of infinitely-divisible distributions in $\mathcal{J}$ with their Lévy measure.

Citation

Download Citation

Sergej Beck. Jochen Blath. Michael Scheutzow. "A new class of large claim size distributions: Definition, properties, and ruin theory." Bernoulli 21 (4) 2457 - 2483, November 2015. https://doi.org/10.3150/14-BEJ651

Information

Received: 1 July 2013; Revised: 1 February 2014; Published: November 2015
First available in Project Euclid: 5 August 2015

zbMATH: 1362.60007
MathSciNet: MR3378474
Digital Object Identifier: 10.3150/14-BEJ651

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability

JOURNAL ARTICLE
27 PAGES


SHARE
Vol.21 • No. 4 • November 2015
Back to Top