Ruin Probability with Parisian Delay for a Spectrally Negative Lévy Risk Process

By Irmina Czarna, Zbigniew Palmowski. Journal of Applied Probability, 2010

87 citations recorded by the source corpus.

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 Cramér-type and convolution-equivalent asymptotics when reserves tend to ∞. Finally, we analyze some explicit examples.

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Citations in the corpus

On magnitude, asymptotics and duration of drawdowns for L\'{e}vy models (2015, background): “ich is the ﬁrst time the length of excursions from a ﬁxed spatial level (rather than its running maximum) exceeds a pre-speciﬁed time threshold; see, e.g., Chesney et al. [9] and Czarna and Palmowski [11]. Further, Loeﬀen et al. [27] provided an uniﬁed proof to derive the probability that the Parisi”
OCCUPATION TIMES OF SPECTRALLY NEGATIVE LÉVY PROCESSES WITH APPLICATIONS (2010, unknown): “More precisely, it is assumed that ruin occurs as soon as an excursion below a critical level is longer than a deterministic time; such models have been studied only very recently in [6, 7, 17] and the idea has been borrowed from finance and Parisian barrier options (see [5]).”
Parisian ruin probability for spectrally negative Lévy processes (2011, methodology): “n time in the case where X is a Brownian motion plus drift and in the case where X is the classical compound Poisson risk process with exponentially distributed claims. Recently, Czarna and Palmowski [4] gave a description of the Parisian ruin probability for a general spectrally negative L´evy proc”
An Insurance Risk Model with Parisian Implementation Delays (2013, unknown): “Therefore, Czarna and Palmowski (2011) and Loeffen et al. (2013) consider the application of an implementation delay in the recognition of an insurer’s capital insufficiency, an idea initially proposed by A. Dassios and S. Wu in a ruin theory context.”