Parisian ruin for the dual risk process in discrete‑time

Zbigniew Palmowski , Lewis Ramsden, Apostolos Papaioannou

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    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 ruin probability. Finally, we explore some interesting special cases, including the binomial/geometric model, and obtain a simple expression for the Parisian ruin probability of the gambler’s ruin problem.
    Original languageEnglish
    Pages (from-to)197-214
    Number of pages18
    JournalEuropean Actuarial Journal
    Volume8
    Issue number1
    Early online date25 Apr 2018
    DOIs
    Publication statusPublished - 1 Jun 2018

    Keywords

    • Binomial/geometric model
    • Discrete-time
    • Dual risk model
    • Parisian gambler’s ruin
    • Parisian ruin
    • Ruin probabilities

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