The probability of ruin
type: Item
instance of: scholarly article
zbMATH Open document ID: 1032.91079
author: Myroslav O. Drozdenko
publication date: 2001-08-09T00:00:00Z
Mathematics Subject Classification ID: 91B30
zbMATH DE Number: 1631963
zbMATH Keywords: ruin probability problem
zbMATH Keywords: classical risk model
MaRDI profile type: Publication
title: The probability of ruin
published in: Theory of Stochastic Processes
review text: The author proposes explicit solutions of the ruin probability problem in the case of the classical risk model. He gives exact formulas for the \(\varphi\left(u\right)\) (probability of no ruin on the infinite time interval with the initial surplus \(u\)) in the case where the distribution function of individual claim \(F\left(x\right)\) is of the hyperexponential type, is the Erlang distribution, is a mixture of the exponential and the generalized binomial distribution. For the discrete distributions the author proposes formulas for determining \(\varphi\left(u\right)\) in the case of Poisson distribution, negative binomial distribution, geometrical distribution, and logarithmic distribution.
reviewed by: M. P. Moklyachuk
description: scientific article; zbMATH DE number 1631963