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RUIN PROBABILITY WITH PARISIAN DELAY FOR A SPECTRALLY NEGATIVE LÉVY RISK PROCESS

IRMINA CZARNA and ZBIGNIEW PALMOWSKI
Journal of Applied Probability
Vol. 48, No. 4 (DECEMBER 2011), pp. 984-1002
Stable URL: http://www.jstor.org/stable/23066438
Page Count: 19
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
RUIN PROBABILITY WITH PARISIAN DELAY FOR A SPECTRALLY NEGATIVE LÉVY RISK PROCESS
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Abstract

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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