Comparison of ruin probability estimates in the presence of heavy tails
type: Item
instance of: scholarly article
title: Comparison of ruin probability estimates in the presence of heavy tails
zbMATH Open document ID: 0978.62099
DOI: 10.1007/BF02365061
author: D. G. Konstantinidis
published in: Journal of Mathematical Sciences (New York)
publication date: 1999-11-22T00:00:00Z
review text: This paper deals with the estimation of the ruin probability in the presence of heavy tails, in a framework in which the claim size distribution is a Pareto one. For this purpose, four methods are presented. The first one, due to Embrechts and Veraverbeke, gives an asymptotic expression for the ruin probability when the initial surplus tends to infinity; the second one, due to Goovaerts and De Vylder, consists in an algorithm that provides two-sided bounds of the ruin probability, obtained by solving the renewal equation through discretization. This method appears particularly suitable in case of small initial capital. By means of the third method, proposed by Willmot and extended by Kalashnikov, it is possible to obtain an upper bound for the ruin probability by means of so-called test functions. By the fourth method, proposed by Kalashnikov, two-sided bounds for the ruin probability are obtained using truncation of random variables. The theoretical treatment is supported by numerical results.
reviewed by: Emilia Di Lorenzo
Mathematics Subject Classification ID: 62P05
Mathematics Subject Classification ID: 91B30
Mathematics Subject Classification ID: 60K10
Mathematics Subject Classification ID: 62G32
zbMATH DE Number: 1295570
zbMATH Keywords: ruin probability
zbMATH Keywords: Pareto distribution
zbMATH Keywords: heavy tails
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02365061
OpenAlex ID: W2002958809
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description: scientific article; zbMATH DE number 1295570