Parisian ruin for the dual risk process in discrete-time

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JournalEuropean Actuarial Journal
DateAccepted/In press - 16 Apr 2018
DateE-pub ahead of print - 25 Apr 2018
DatePublished (current) - Jun 2018
Issue number1
Volume8
Pages (from-to)197-214
Early online date25/04/18
Original languageEnglish

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.

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© The Author(s) 2018.

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