Ruin probabilities of a surplus process described by PDMPs
type: Item
instance of: scholarly article
title: Ruin probabilities of a surplus process described by PDMPs
zbMATH Open document ID: 1141.91027
author: Jing-Min He
author: Rong Wu
author: Huayue Zhang
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 2008-05-26T00:00:00Z
review text: The class of risk processes described by a piecewise deterministic Markov process is considered, i.e. between claim arrivals epochs the process follows a deterministic path described by a measurable continuously differentiable function. An integro-differential equation for the ultimate ruin probability for the surplus process is derived. Under a certain assumption, it is transformed into the ruin probability of a risk process whose premiums depend on the current reserves. Then the ruin probability and its upper bounds are obtained using change of the probability measure and local adjustment coefficients. The example is considered when the claim-size is exponentially distributed.
reviewed by: Yuliya S. Mishura
Mathematics Subject Classification ID: 91B30
Mathematics Subject Classification ID: 60J25
zbMATH DE Number: 5278778
zbMATH Keywords: surplus process
zbMATH Keywords: piecewise deterministic Markov process
zbMATH Keywords: integro-differential equation
zbMATH Keywords: exponentially distributed claim size
MaRDI profile type: Publication
full work available at URL: s10255-006-6137-8
OpenAlex ID: W2014221666
cites work: Q4379506
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cites work: Ruin theory for the risk process described by PDMPs
DOI: 10.1007/S10255-006-6137-8
description: scientific article; zbMATH DE number 5278778