 A note on killing with applications in risk theoryJevgenijs Ivanovs Insurance: Mathematics and Economics, 2013, vol. 52, issue 1, 29-34 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 Lévy 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 (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:52:y:2013:i:1:p:29-34 DOI: 10.1016/j.insmatheco.2012.10.005 Access Statistics for this article Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu More articles in Insurance: Mathematics and Economics from Elsevier |
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