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Ruin probability with Parisian delay for a spectrally negative Lévy risk process. (English) Zbl 1232.60036
The authors consider the so-called Parisian ruin probability which arises when the surplus process stays below 0 longer than a fixed amount of time. For general spectrally negative Lévy insurance risk processes they derive an expression for the ruin probability in terms of quantities that can be calculated explicitly in many models. Cramér-type and convolution-equivalent asymptotics of the Parisian ruin probability when reserves tend to infinity are derived. Some explicit examples are analyzed.

60G51 Processes with independent increments; Lévy processes
93E20 Optimal stochastic control
60J99 Markov processes
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