Parisian types of ruin probabilities for a class of dependent risk-reserve processes

Mogens Bladt*, Bo Friis Nielsen, Oscar Peralta

*Corresponding author for this work

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Abstract

For a rather general class of risk-reserve processes, we provide an exact method for calculating different kinds of ruin probabilities, with particular emphasis on variations over Parisian type of ruin. The risk-reserve processes under consideration have, in general, dependent phase-type distributed claim sizes and inter-arrivals times, whereas the movement between claims can either be linear or follow a Brownian motion with linear drift. For such processes, we provide explicit formulae for classical, Parisian and cumulative Parisian types of ruin (for both finite and infinite time horizons) when the clocks are phase-type distributed. An erlangization scheme provides an efficient algorithmic methods for calculating the aforementioned ruin probabilities with deterministic clocks. Special attention is drawn to the construction of specific dependency structures, and we provide a number of numerical examples to study its effect on probabilities.

Original languageEnglish
JournalScandinavian Actuarial Journal
Volume2019
Issue number1
Pages (from-to)32-61
ISSN0346-1238
DOIs
Publication statusPublished - 2018

Keywords

  • Sparre-Andersen
  • Brownian motion
  • Ruin probability
  • (cumulative) Parisian ruin
  • Fluid Flow
  • Order statistics
  • Dependency
  • Baker copula
  • Phase-type distributions
  • Erlangization
  • Lévy process

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