A note on killing with applications in risk theory

Details

Serval ID
serval:BIB_9947710F504B
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
A note on killing with applications in risk theory
Journal
Insurance: Mathematics and Economics
Author(s)
Ivanovs J.
ISSN
0167-6687
Publication state
Published
Issued date
2013
Peer-reviewed
Oui
Volume
52
Number
1
Pages
29-34
Language
english
Abstract
It is often natural to consider defective or killed stochastic processes. Various observations continue to hold true for this wider class of processes yielding more general results in a transparent way without additional effort. We illustrate this point with an example from risk theory by showing that the ruin probability for a defective risk process can be seen as a triple transform of various quantities of interest on the event of ruin. In particular, this observation is used to identify the triple transform in a simple way when either claims or interarrivals are exponential. We also show how to extend these results to modulated risk processes, where exponential distributions are replaced by phase-type distributions. In addition, we review and streamline some basic exit identities for defective Levy and Markov additive processes.
Keywords
Killing, Defective process, Transform, Ruin probability, Time to ruin, Deficit at ruin, Gerber-Shiu penalty function, Phase-type distribution, Modulation
Web of science
Create date
13/02/2014 15:48
Last modification date
21/08/2019 6:12
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