The moments of the discounted loss and the discounted dividends for a spectrally negative Lévy risk process

Research output: Contribution to journalArticlepeer-review

Abstract

Consider a spectrally negative risk process where, on ruin, the deficit is immediately paid, and the process restarts from 0. When the process reaches a threshold b, all the surplus above b is paid as dividend. Applying the theory of exit times for a spectrally negative Lévy process and its reflection at the maximum and at the minimum, we obtain recursive formulae for the following moments. (i) The moments of the discounted loss until the process reaches b. This is equivalent to the moments of the discounted dividends in the dual model under the barrier strategy. (ii) The moments of the discounted loss for models with and without a dividend barrier for the infinite horizon. (iii) The moments of the discounted dividends for the infinite horizon.

Original languageEnglish
Pages (from-to)665-687
Number of pages23
JournalJournal of Applied Probability
Volume52
Issue number3
DOIs
StatePublished - Sep 2015

Bibliographical note

Publisher Copyright:
© 2015 Applied Probability Trust.

Keywords

  • Barrier strategy
  • Capital injection
  • Dividends
  • Dual model
  • Exit times
  • Reflected process
  • Scale function

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (all)
  • Statistics, Probability and Uncertainty

Fingerprint

Dive into the research topics of 'The moments of the discounted loss and the discounted dividends for a spectrally negative Lévy risk process'. Together they form a unique fingerprint.

Cite this