Ruin probability with Parisian delay for a spectrally negative L 'evy\n risk process

2010/03/22 by Irmina Czarna, Czarna, Irmina, Zbigniew Palmowski +1
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #FOS: Economics and business #FOS: Mathematics #Insurance and Financial Risk Management #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Probability and Risk Models #Risk Management (q-fin.RM)

paper · pdf · doi:10.48550/arxiv.1003.4299

openalex publication_date 2010/03/22 · openalex created_date 2023/02/18 · openalex updated_date 2026/07/28

Abstract

In this paper we analyze so-called Parisian ruin probability that happens\nwhen surplus process stays below zero longer than fixed amount of time\n\ζ>0. We focus on general spectrally negative L 'evy insurance risk\nprocess. For this class of processes we identify expression for ruin\nprobability in terms of some other quantities that could be possibly calculated\nexplicitly in many models. We find its Cram 'er-type and\nconvolution-equivalent asymptotics when reserves tends to infinity. Finally, we\nanalyze few explicit examples.\n

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