Porównanie prawdopodobieństw paryskiej i klasycznej ruiny dla procesu ryzyka typu Lévy’ego
Comparison of Parisian and classical ruin probabilities for a Lévy risk process

Summary/Abstract: In this paper we analyze so-called Parisian ruin probability that happens when surplus process stays below zero longer than fixed amount of time . > 0. We focus on general spectrally negative Lévy insurance risk process. For this class of processes we identify expression for (classical and Parsisan) ruin probability in terms of so-called scale functions which is defined via Laplace exponent of risk process. We analyze few explicit examples such as Cramér-Lunberg process (large claim size case) and Brownian motion with drift (small claim size case). In this paper we numerically compare classical and Parisian ruin probabilities.

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