Bounds for classical ruin probabilities
type: Item
instance of: scholarly article
title: Bounds for classical ruin probabilities
zbMATH Open document ID: 0547.62068
DOI: 10.1016/0167-6687(84)90050-7
published in: Insurance Mathematics \& Economics
publication date: 1984-01-01T00:00:00Z
review text: This paper derives upper and lower bounds for the ruin probability over infinite time. The key observation is that if \(u=k*(1-u),\) then \(v-u=(v- k*(1-v))*(1-u),\) where \((f*g)(x)=\int^{x}_{0}f(x-y)dg(y)\). Applications to sub-exponential distributions are also given.
Mathematics Subject Classification ID: 62P05
zbMATH DE Number: 3872523
zbMATH Keywords: collective risk theory
zbMATH Keywords: convolution
zbMATH Keywords: renewal equation
zbMATH Keywords: Poisson claim number process
zbMATH Keywords: bounds
zbMATH Keywords: ruin probability over infinite time
zbMATH Keywords: sub- exponential distributions
author: Floriaen E. C. De Vylder
author: Marc J. Goovaerts
reviewed by: E. S. W. Shiu
MaRDI profile type: Publication
full work available at URL: 0167-6687(84)90050-7
OpenAlex ID: W1972738543
cites work: Q5674726
cites work: Q5601945
cites work: Subexponentiality and infinite divisibility
cites work: Estimates for the probability of ruin with special emphasis on the possibility of large claims
cites work: Use of differential and integral inequalities to bound ruin and queuing probabilities
cites work: The class of subexponential distributions
cites work: Asymptotic behaviour of Wiener-Hopf factors of a random walk
description: scientific article; zbMATH DE number 3872523