On occupation times in the red of Lévy risk models

David Landriault, Bin Li and Mohamed Amine Lkabous

Insurance: Mathematics and Economics, 2020, vol. 92, issue C, 17-26

Abstract: In this paper, we obtain analytical expression for the distribution of the occupation time in the red (below level 0) up to an (independent) exponential horizon for spectrally negative Lévy risk processes and refracted spectrally negative Lévy risk processes. This result improves the existing literature in which only the Laplace transforms are known. Due to the close connection between occupation time and many other quantities, we provide a few applications of our results including future drawdown, inverse occupation time, Parisian ruin with exponential delay, and the last time at running maximum.

Keywords: Occupation time; Inverse occupation time; Parisian ruin; Lévy insurance risk processes; Scale functions (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:92:y:2020:i:c:p:17-26

DOI: 10.1016/j.insmatheco.2020.02.011

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