Gerber-Shiu functionals at Parisian ruin for Lévy insurance risk processes

2014/07/25 by Erik J. Baurdoux, Juan Carlos Pardo, Baurdoux, E. J. +5
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #60G51 #60J99 #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1407.6785

openalex publication_date 2014/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Inspired by works of Landriault et al. \citeLRZ-0, LRZ, we study discounted penalties at ruin for surplus dynamics driven by a spectrally negative Lévy process with Parisian implementation delays. To be specific, we study the so-called Gerber-Shiu functional for a ruin model where at each time the surplus process goes negative, an independent exponential clock with rate q>0 is started. If the clock rings before the surplus becomes positive again then the insurance company is ruined. Our methodology uses excursion theory for spectrally negative Lévy processes and relies on the theory of the so-called scale functions. In particular, our results extend recent results of Landriault et al. \citeLRZ-0, LRZ.

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