Strikingly simple identities relating exit problems for Lévy processes under continuous and Poisson observations

Hansjörg Albrecher and Jevgenijs Ivanovs

Stochastic Processes and their Applications, 2017, vol. 127, issue 2, 643-656

Abstract: We consider exit problems for general Lévy processes, where the first passage over a threshold is detected either immediately or at an epoch of an independent homogeneous Poisson process. It is shown that the two corresponding one-sided problems are related through a surprisingly simple identity. Moreover, we identify a simple link between two-sided exit problems with one continuous and one Poisson exit. Finally, identities for reflected processes and a link between some Parisian type exit problems are established. For spectrally one-sided Lévy processes this approach enables alternative proofs for a number of previously established identities, providing additional insight.

Keywords: Lévy processes; Exit problems; Poisson observation; Occupation times; Parisian ruin (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (12)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:127:y:2017:i:2:p:643-656

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DOI: 10.1016/j.spa.2016.06.021

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