Parisian ruin for the dual risk process in discrete-time



Palmowski, Zbigniew, Ramsden, Lewis and Papaioannou, Apostolos D
(2018) Parisian ruin for the dual risk process in discrete-time. European Actuarial Journal, 8 (1). pp. 197-214.

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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.

Item Type: Article
Uncontrolled Keywords: dual risk model, discrete-time, ruin probabilities, Parisian ruin, binomial/geometric model, Parisian gambler’s ruin
Depositing User: Symplectic Admin
Date Deposited: 25 Apr 2018 06:31
Last Modified: 19 Jan 2023 06:35
DOI: 10.1007/s13385-018-0172-8
Open Access URL: https://link.springer.com/content/pdf/10.1007/s133...
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URI: https://livrepository.liverpool.ac.uk/id/eprint/3020565