Parisian ruin for a refracted L\'evy process
Probability
2017-03-08 v2 Risk Management
Abstract
In this paper, we investigate Parisian ruin for a L\'evy surplus process with an adaptive premium rate, namely a refracted L\'evy process. More general Parisian boundary-crossing problems with a deterministic implementation delay are also considered. Our main contribution is a generalization of the result in Loeffen et al. (2013) for the probability of Parisian ruin of a standard L\'evy insurance risk process. Despite the more general setup considered here, our main result is as compact and has a similar structure. Examples are provided.
Cite
@article{arxiv.1603.09324,
title = {Parisian ruin for a refracted L\'evy process},
author = {Mohamed Amine Lkabous and Irmina Czarna and Jean-François Renaud},
journal= {arXiv preprint arXiv:1603.09324},
year = {2017}
}
Comments
Typos corrected; proof of Theorem 2 fixed; numerical examples added