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 ...
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
30 references, page 1 of 2

Albrecher, H, Badescu, A, Landriault, D. On the dual risk model with tax payments. Insur Math Econ. 2008; 42 (3): 1086-1094 [OpenAIRE] [DOI]

Asmussen, S. Applied probability and queues. 2003

Asmussen, S, Albrecher, H. Ruin probabilities. 2010

Avanzi, B, Gerber, HU, Shiu, ES. Optimal dividends in the dual model. Insur Math Econ. 2007; 41 (1): 111-123 [OpenAIRE] [DOI]

5.Bergel AI, Rodríguez-Martínez EV, Egídio dos Reis AD (2016) On dividends in the phase-type dual risk model. Scand Actuar J. 10.1080/03461238.2016.1252944

Boudreault, M, Cossette, H, Landriault, D, Marceau, E. On a risk model with dependence between interclaim arrivals and claim sizes. Scand Actuar J. 2006; 2006 (5): 265-285 [OpenAIRE] [DOI]

Cheng, S, Gerber, HU, Shiu, ES. Discounted probabilities and ruin theory in the compound binomial model. Insur Math Econ. 2000; 26 (2): 239-250 [DOI]

Chesney, M, Jeanblanc-Picque, M, Yor, M. Brownian excursions and Parisian barrier options. Adv Appl Prob. 1997; 29: 165-184 [OpenAIRE] [DOI]

Cheung, EC, Drekic, S. Dividend moments in the dual risk model: exact and approximate approaches. Astin Bull. 2008; 38 (02): 399-422 [OpenAIRE] [DOI]

Cossette, H, Landriault, D, Marceau, É. Ruin probabilities in the compound Markov binomial model. Scand Actuar J. 2003; 2003 (4): 301-323 [OpenAIRE] [DOI]

Cossette, H, Landriault, D, Marceau, É. Exact expressions and upper bound for ruin probabilities in the compound Markov binomial model. Insur Math Econ. 2004; 34 (3): 449-466 [OpenAIRE] [DOI]

Czarna, I, Palmowski, Z. Ruin probability with Parisian delay for a spectrally negative Lévy risk process. J Appl Prob. 2011; 48 (04): 984-1002 [OpenAIRE] [DOI]

Czarna, I, Palmowski, Z, Świa̧tek, P. Discrete time ruin probability with Parisian delay. Scand Actuar J. 2016 [OpenAIRE]

14.Dassios A, Wu S (2008) Parisian ruin with exponential claims. Department of Statistics, London School of Economics and Political Science, London, UK. (Unpublished)

Dickson, DC. Some comments on the compound binomial model. Astin Bull. 1994; 24 (01): 33-45 [DOI]

30 references, page 1 of 2
Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue
publication . Article . Preprint . 2018

Parisian ruin for the dual risk process in discrete-time

Zbigniew Palmowski; Lewis Ramsden; Apostolos D. Papaioannou;