A risk model with an observer in a Markov environment

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Serval ID
serval:BIB_07934B6E1EC0
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
A risk model with an observer in a Markov environment
Journal
Risks
Author(s)
Albrecher H., Ivanovs J.
ISSN
2227-9091
Publication state
Published
Issued date
11/2013
Peer-reviewed
Oui
Volume
1
Number
3
Pages
148-161
Language
english
Abstract
We consider a spectrally-negative Markov additive process as a model of a risk process in a random environment. Following recent interest in alternative ruin concepts, we assume that ruin occurs when an independent Poissonian observer sees the process as negative, where the observation rate may depend on the state of the environment. Using an approximation argument and spectral theory, we establish an explicit formula for the resulting survival probabilities in this general setting. We also discuss an efficient evaluation of the involved quantities and provide a numerical illustration.
Keywords
Markov additive process, level-crossing probabilities, Poissonian observation, ruin probability, occupation times
Open Access
Yes
Create date
05/11/2013 15:25
Last modification date
20/08/2019 12:29
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