Stochastic bounds for the Sparre Andersen process
type: Item
instance of: scholarly article
title: Stochastic bounds for the Sparre Andersen process
zbMATH Open document ID: 1092.60035
author: Franco Pellerey
author: Cristina Zucca
published in: Methodology and Computing in Applied Probability
publication date: 2006-01-30T00:00:00Z
review text: Let \(X(j)\), \(j>0\), be independent and identically distributed random variables, and let \(N(t)\) be a counting process, independent of the \(X(j)\). The random sum \(S(t)\) of the first \(N(t)\) members of the sequence \(X(j)\) is frequently appearing in the actuarial and insurance literature. \(S(t)\) is called a Sparre Andersen process if \(N\) is a renewal process. Computation with \(S(t)\) is usually difficult, due to the lack of knowledge on \(X(j)\) and \(N(t)\). The authors set stochastic bounds on \(S(t)\) which bounds are computable. Several examples are given, and the sharpness of the bounds is discussed.
Mathematics Subject Classification ID: 60K10
Mathematics Subject Classification ID: 60E15
zbMATH DE Number: 5002466
zbMATH Keywords: stochastic order
zbMATH Keywords: convex order
zbMATH Keywords: positive dependence
zbMATH Keywords: ruin probabilities
reviewed by: Janos Galambos
MaRDI profile type: Publication
full work available at URL: s11009-005-1484-0
OpenAlex ID: W2054883989
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DOI: 10.1007/S11009-005-1484-0
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description: scientific article; zbMATH DE number 5002466