Drawdown analysis for the renewal insurance risk process

David Landriault, Bin Li, Shu Li

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we study some drawdown-related quantities in the context of the renewal insurance risk process with general interarrival times and phase-type distributed jump sizes. We make use of some recent results on the two-sided exit problem for the spectrally negative Markov additive process and a fluid flow analogy between certain queues and risk processes to solve for the two-sided exit problem of the renewal insurance risk process. The two-sided exit quantities are later shown to be central to the analysis of drawdown quantities including the drawdown time, the drawdown size, the running maximum (minimum) at the drawdown time, the last running maximum time prior to drawdown, the number of jumps before drawdown and the number of excursions from running maximum before drawdown. Finally, we consider another application of our methodology for the study of the expected discounted dividend payments until ruin.

Original languageEnglish (US)
Pages (from-to)267-285
Number of pages19
JournalScandinavian Actuarial Journal
Volume2017
Issue number3
DOIs
StatePublished - Mar 16 2017

Keywords

  • constant dividend barrier strategy
  • drawdown
  • fluid flow technique
  • renewal insurance risk process
  • ruin probability
  • two-sided exit problem

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

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