Parisian quasi-stationary distributions for asymmetric Lévy processes

Irmina Czarna and Zbigniew Palmowski

Statistics & Probability Letters, 2017, vol. 127, issue C, 75-84

Abstract: In recent years there has been some focus on quasi-stationary behavior of an one-dimensional Lévy process X, where we ask for the law P(Xt∈dy|τ0−>t) for t→∞ and τ0−=inf{t≥0:Xt<0}. In this paper we address the same question for so-called Parisian ruin time τθ, that happens when process stays below zero longer than independent exponential random variable with intensity θ.

Keywords: Quasi-stationary distribution; Lévy process; Risk process; Ruin probability; Asymptotics; Parisian ruin (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.spl.2017.03.011

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