The approximations of the ruin probability in classical risk model
type: Item
instance of: scholarly article
zbMATH Open document ID: 0973.91049
author: Victor Shpyrko
publication date: 2001-09-16T00:00:00Z
Mathematics Subject Classification ID: 91B30
zbMATH DE Number: 1646495
zbMATH Keywords: ruin probability
zbMATH Keywords: classical risk model
zbMATH Keywords: insurance claims
zbMATH Keywords: approximation
MaRDI profile type: Publication
title: The approximations of the ruin probability in classical risk model
published in: Theory of Stochastic Processes
review text: The paper deals with approximated evaluations of the ruin probability in the classical risk model. The author gives the description of the classical risk model and the corresponding Cramér-Lundberg approximation and the inequality for the ruin probability. Then Beekman-Bowers approximation, De Vylder approximation, diffusion approximation and comparison of these approximations are presented. For the comparison of the approximations the relative error of the approximation \(\varepsilon(u)=(\bar\psi (u)-\psi(u))/\psi(u)\) is applied. Here \(\psi(u)\) is the ruin probability, \(\bar\psi(u)\) is the corresponding approximation of the ruin probability. The practical applications of the ruin probability approximations for 30 Ukrainian insurance companies in the cases of exponential distribution and Gamma distribution of insurance payments are considered.
reviewed by: Aleksandr D. Borisenko
description: scientific article; zbMATH DE number 1646495