Parisian ruin for the dual risk process in discrete-time

2017/08/19 by Zbigniew Palmowski, Palmowski, Zbigniew, Lewis Ramsden +3
Mathematics · #62P05 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:62P05

paper · pdf · doi:10.48550/arxiv.1708.06785

arxiv created 2017/08/19 · arxiv updated 2017/08/24

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 fnite-time Parisian ruin probability, in terms of classic discrete-time dual ruin probabilities. Moreover, we obtain an explicit expression for the corresponding infnite-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 infnite-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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