The expected discounted penalty function under a risk model with stochastic income
type: Item
instance of: scholarly article
title: The expected discounted penalty function under a risk model with stochastic income
zbMATH Open document ID: 1181.91100
author: Chantal Labbé
author: Kristina P. Sendova
published in: Applied Mathematics and Computation
publication date: 2009-12-16T00:00:00Z
review text: The paper deals with a ruin model framed within the general scenario of the expected discounted penalty function, where premiums and claims follow compound Poisson processes. In this framework the authors deduce a defective renewal equation and an integral equation involving the expected penalty function; in particular explicit expressions of such functions are given in some special cases. Moreover, assuming that premiums follow the Erlang\((n, \beta)\) distribution, the authors specialize the defective renewal equation for the expected discounted penalty function. The theoretical results are applied to specific examples under particular hypotheses on claims and premiums.
reviewed by: Emilia Di Lorenzo
Mathematics Subject Classification ID: 91B30
Mathematics Subject Classification ID: 60K05
zbMATH DE Number: 5648695
zbMATH Keywords: defective renewal equation
zbMATH Keywords: Erlang\((n, \beta)\) premium distribution
zbMATH Keywords: expected discounted penalty function
zbMATH Keywords: probability of ruin
zbMATH Keywords: Laplace transform of the time to ruin
MaRDI profile type: Publication
full work available at URL: j.amc.2009.07.049
OpenAlex ID: W1970455908
cites work: Q3661894
cites work: The expected discounted penalty at ruin in the risk process with random income
cites work: The Gerber-Shiu discounted penalty function in the delayed renewal risk process with random income
cites work: Q4442928
cites work: A Note on Negative Customers, GI/G/1 Workload, and Risk Processes
cites work: On the time to ruin for Erlang(2) risk processes.
cites work: The Time Value of Ruin in a Sparre Andersen Model
cites work: On the Time Value of Ruin
cites work: Moments for first-passage and last-exit times, the minimum, and related quantities for random walks with positive drift
cites work: On the modification of Rouche's theorem for the queueing theory problems
cites work: Introductory lectures on fluctuations of Lévy processes with applications.
cites work: On ruin for the Erlang \((n)\) risk process
cites work: Analysis of a defective renewal equation arising in ruin theory
cites work: Q3137759
cites work: Q4435489
cites work: Risk process with random income
cites work: On the discounted penalty function in the renewal risk model with general interclaim times
cites work: Lundberg inequalities for renewal equations
DOI: 10.1016/J.AMC.2009.07.049
description: scientific article; zbMATH DE number 5648695