On \(s\)-convex stochastic extrema for arithmetic risks
type: Item
instance of: scholarly article
title: On \(s\)-convex stochastic extrema for arithmetic risks
zbMATH Open document ID: 1006.91041
DOI: 10.1016/S0167-6687(99)00030-X
published in: Insurance Mathematics \& Economics
publication date: 2000-03-30T00:00:00Z
review text: The authors deal with a class of discrete stochastic orderings in the space of random variables. In particular, they follow (their as well as the others authors) former results on this topic. A brief survey of the former results is given in the introduction. After the introduction the authors, first, recall the definition of \(s\)-convex discrete stochastic orderings. The aim of the paper is to construct the extremal (minimal and maximal) distributions with respect to the introduced \(s\)-convex orderings. To this end, first, the general problem of bounding risks is studied. Furthermore, special attention is paid the case when the risks are known to have a decreasing density function. Surely, the investigated problem of stochastic orderings is rather important from the applications point of the view. At the end of the paper, the presented results are applied to obtain the eventual ruin probability in the compound binomial risk process.
Mathematics Subject Classification ID: 91B30
Mathematics Subject Classification ID: 60E15
zbMATH DE Number: 1396353
zbMATH Keywords: discrete stochastic orderings
zbMATH Keywords: ruin probability
zbMATH Keywords: compound binomial risk process
author: Michel Denuit
author: Claude Lefèvre
author: Mhamed Mesfioui
reviewed by: Vlasta Kaňková
MaRDI profile type: Publication
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Wikidata QID: Q126311171
full work available at URL: s0167-6687(99)00030-x
OpenAlex ID: W2080645034
description: scientific article; zbMATH DE number 1396353