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Abstract
In this paper we evaluate the probability of the discrete time Parisian ruin that occurs when surplus process stays below or at zero at least for some fixed duration of time . We identify expressions for the ruin probabilities within finite and infinite-time horizon. We also find their light and heavy-tailed asymptotics when initial reserves approach infinity. Finally, we calculate these probabilities for a few explicit examples.
Notes
No potential conflict of interest was reported by the authors.
Additional information
Funding
This work is partially supported by National Science Centre [grant number DEC-2011/01/B/HS4/00982] (2012–2013). All authors was partially supported by project RARE -318984, a Marie Curie IRSES Fellowship within the 7th European Community Framework Programme. Zbigniew Palmowski was partially supported by National Science Centre of Poland (NCN) under grant 2011/01/B/HS4/00982. Irmina Czarna was partially supported by National Science Centre of Poland (NCN) under grant 2015/19/D/ST1/01182.