On the expected discounted penalty function for a perturbed risk process driven by a subordinator
type: Item
instance of: scholarly article
title: On the expected discounted penalty function for a perturbed risk process driven by a subordinator
zbMATH Open document ID: 1130.91032
author: Manuel Morales
published in: Insurance Mathematics \& Economics
publication date: 2007-09-03T00:00:00Z
review text: The author considers the following perturbed risk model: \(U(t)=u+ct-S(t)+W(t)\), where \(S\) is a subordinator with zero drift and Lévy measure \(\nu\) and \(W\) is a zero-drift Brownian motion with infinitesimal variance \(\sigma^2\). The parameter \(u\) is an initial surplus and \(c\) is a constant premium rate. The purpose of the paper is to show that the expected discounted penalty function for this risk model satisfies a defective renewal equation. The stepping stone to produce the main result is the construction of a family of compound Poisson processes converging weakly to any given subordinator. The results allow for a wide range of models for the aggregate claims process, in particular those closed-form expressions are available like the gamma and inverse Gaussian processes. These results are possible due to the Lévy structure of the risk process.
reviewed by: Yuliya S. Mishura
Mathematics Subject Classification ID: 91B30
Mathematics Subject Classification ID: 60K10
Mathematics Subject Classification ID: 60K05
zbMATH DE Number: 5186582
zbMATH Keywords: Lévy processes
zbMATH Keywords: renewal equations
MaRDI profile type: Publication
full work available at URL: j.insmatheco.2006.04.008
OpenAlex ID: W2066640641
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DOI: 10.1016/J.INSMATHECO.2006.04.008
description: scientific article; zbMATH DE number 5186582