Self-similar processes in collective risk theory
type: Item
instance of: scholarly article
title: Self-similar processes in collective risk theory
zbMATH Open document ID: 0937.60029
DOI: 10.1155/S1048953398000367
author: Zbigniew Michna
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 2000-06-07T00:00:00Z
full work available at URL: https://eudml.org/doc/48419
review text: Conditions are given for an insurance risk process to converge weakly to a long-range dependent process, in particular fractional Brownian motion. Convergence of the associated ruin probabilities is discussed and various estimates of the ruin probabilities for fractional Brownian motion are given. The occurrence of long-range dependence in insurance risk is motivated by an example with alternating periods of safe and risky conditions, along the lines of \textit{D. Heath}, \textit{S. Resnick} and \textit{G. Samorodnitsky} [Ann. Appl. Probab. 9, No. 2, 352-375 (1999)].
reviewed by: Søren Asmussen
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60G70
Mathematics Subject Classification ID: 91B30
zbMATH DE Number: 1247733
zbMATH Keywords: alternating renewal process
zbMATH Keywords: fractional Brownian motion
zbMATH Keywords: functional central limit theorem
zbMATH Keywords: Hermite rank
zbMATH Keywords: long-range dependence
zbMATH Keywords: ruin probability
zbMATH Keywords: Skorokhod topology
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1247733