Parisian Ruin with Erlang Delay and a Lower Bankruptcy Barrier

Esther Frostig, Adva Keren-Pinhasik

Research output: Contribution to journalArticlepeer-review

Abstract

Parisian ruin occurs once the surplus stays continuously below zero for a given period. We consider the spectrally negative Lévy risk process where ruin is declared either at the first time that the reserve stays continuously below zero for an exponentially or mixed Erlang distributed random variable, or once it reaches a given negative threshold. We consider the Laplace transform of the time to ruin and the Laplace transform of the time that the process is negative.

Original languageEnglish
Pages (from-to)101-134
Number of pages34
JournalMethodology and Computing in Applied Probability
Volume22
Issue number1
DOIs
StatePublished - 1 Mar 2020

Bibliographical note

Funding Information:
The research of Esther Frostig was supported by the Israel Science Foundation (Grant No. 1999/19).

Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

  • Exit times
  • Laplace transform
  • Risk process
  • Ruin probability

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (all)

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