publication . Article . Preprint . 2018

# Parisian ruin for the dual risk process in discrete-time

Zbigniew Palmowski; Lewis Ramsden; Apostolos D. Papaioannou;
Open Access English
• Published: 01 Jun 2018 Journal: European Actuarial Journal, volume 8, issue 1, pages 197-214 (issn: 2190-9733, eissn: 2190-9741, Copyright policy)
• Publisher: Springer Berlin Heidelberg
• Country: United Kingdom
Abstract
In this paper we consider the Parisian ruin probabilities for the dual risk model in a discrete-time setting. By exploiting the strong Markov property of the risk process we derive a recursive expression for the finite-time Parisian ruin probability, in terms of classic discrete-time dual ruin probabilities. Moreover, we obtain an explicit expression for the corresponding infinite-time Parisian ruin probability as a limiting case. In order to obtain more analytic results, we employ a conditioning argument and derive a new expression for the classic infinite-time ruin probability in the dual risk model and hence, an alternative form of the infinite-time Parisian ...
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Subjects
arXiv: Mathematics::ProbabilityMathematics::Optimization and ControlComputer Science::Systems and Control
free text keywords: Original Research Paper, Dual risk model, Discrete-time, Ruin probabilities, Parisian ruin, Binomial/geometric model, Parisian gambler’s ruin, Mathematics - Probability, 62P05, Statistics, Probability and Uncertainty, Economics and Econometrics, Statistics and Probability, Discrete time and continuous time, Recursion, Mathematical finance, Risk model, Binomial, Risk process, Markov property, Mathematical economics, Mathematics, Limiting
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