Parisian ruin probability for Markov additive risk processes
نویسندگان
چکیده
منابع مشابه
Parisian Ruin Probability for Spectrally Negative Lévy Processes
In this note we give, for a spectrally negative Lévy process, a compact formula for the Parisian ruin probability, which is defined by the probability that the process exhibits an excursion below zero which length exceeds a certain fixed period r. The formula involves only the scale function of the spectrally negative Lévy process and the distribution of the process at time r.
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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 d > 0. 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 p...
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In this paper we analyze the so-called Parisian ruin probability, which arises when the surplus process stays below 0 longer than a fixed amount of time ζ > 0. We focus on a general spectrally negative Lévy insurance risk process. For this class of processes, we derive an expression for the ruin probability in terms of quantities that can be calculated explicitly in many models. We find its Cra...
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ژورنال
عنوان ژورنال: Advances in Difference Equations
سال: 2018
ISSN: 1687-1847
DOI: 10.1186/s13662-018-1600-4