Some Expressions of a Generalized Version of the Expected Time in the Red and the Expected Area in Red

Julien Callant, Julien Trufin, Pierre Zuyderhoff

Research output: Journal PublicationArticlepeer-review

Abstract

In this paper, we study a generalized version of the expected time in the red and the expected area in red introduced in Loisel (2005). We derive some expressions for this risk measure both in light tailed and heavy tailed cases for general risk processes. Then, some further expressions are obtained for Lévy processes together with an upper bound in the light-tailed case and an additional result for large initial capitals in the subexponential case.

Original languageEnglish
Pages (from-to)595-611
Number of pages17
JournalMethodology and Computing in Applied Probability
Volume24
Issue number2
DOIs
Publication statusPublished - Jun 2022
Externally publishedYes

Keywords

  • Asymptotic behavior
  • Expected area in red
  • Expected time in the red
  • Lévy processes
  • Upper bound

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (all)

Fingerprint

Dive into the research topics of 'Some Expressions of a Generalized Version of the Expected Time in the Red and the Expected Area in Red'. Together they form a unique fingerprint.

Cite this