5 papers · 1 filter
On the longest/shortest negative excursion of a Lévy risk process and related quantities
M. A. Lkabous, Z. Palmowski
In this paper, we analyze some distributions involving the longest and shortest negative excursions of spectrally negative Lévy processes using the binomial expansion approach. Mor…
A note on Parisian ruin under a hybrid observation scheme
Mohamed Amine Lkabous
In this paper, we study the concept of Parisian ruin under the hybrid observation scheme model introduced by Li et al. \cite{binetal2016}. Under this model, the process is observed…
Poissonian occupation times of spectrally negative Lévy processes with applications
Mohamed Amine Lkabous
In this paper, we introduce the concept of \emph{Poissonian occupation times} below level of spectrally negative Lévy processes. In this case, occupation time is accumulated on…
A unified approach to ruin probabilities with delays for spectrally negative Lévy processes
Mohamed Amine Lkabous, Jean-François Renaud
In this paper, we unify two popular approaches for the definition of actuarial ruin with implementation delays, also known as Parisian ruin. Our new definition of ruin includes bot…
Parisian ruin for a refracted Lévy process
Mohamed Amine Lkabous, Irmina Czarna, Jean-François Renaud
In this paper, we investigate Parisian ruin for a Lévy surplus process with an adaptive premium rate, namely a refracted Lévy process. More general Parisian boundary-crossing probl…