English

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

R2 v1 2026-06-22T13:21:45.550Z