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Fractional Poisson process: long-range dependence and applications in ruin theory
Multi angle
Authors : Biard, Romain (Author of the conference)
CIRM (Publisher )
60G55 - Point processes
60K05 - Renewal theory
91B30 - Risk theory, insurance
33E12 - Mittag-Leffler functions and generalizations
60G22 - Fractional processes, including fractional Brownian motion
CIRM (Publisher )
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Abstract :
We study a renewal risk model in which the surplus process of the insurance company is modeled by a compound fractional Poisson process. We establish the long-range dependence property of this non-stationary process. Some results for the ruin probabilities are presented in various assumptions on the distribution of the claim sizes.
Keywords : fractional Poisson process; renewal process; long-range dependence; ruin probability
MSC Codes : Keywords : fractional Poisson process; renewal process; long-range dependence; ruin probability
60G55 - Point processes
60K05 - Renewal theory
91B30 - Risk theory, insurance
33E12 - Mittag-Leffler functions and generalizations
60G22 - Fractional processes, including fractional Brownian motion
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 08/03/16 Conference Date : 23/02/16 Subseries : Research talks arXiv category : Probability Mathematical Area(s) : Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:24:38 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2016-02-23_Biard.mp4 
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Information on the Event
Event Title : Thematic month on statistics - Week 4: Extremes, copulas and actuarial science / Mois thématique sur les statistiques - Semaine 4 : Extrêmes, copules et actuariatEvent Organizers : Boutahar, Mohamed ; Pommeret, Denys ; Royer-Carenzi, Manuela Dates : 22/02/16 - 26/02/16 Event Year : 2016 Event URL : http://conferences.cirm-math.fr/1618.html
Citation Data
DOI : 10.24350/CIRM.V.18933903Cite this video as: Biard, Romain (2016). Fractional Poisson process: long-range dependence and applications in ruin theory. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18933903 URI : http://dx.doi.org/10.24350/CIRM.V.18933903 |
See Also
- [Multi angle] On tail dependence coefficients of transformed multivariate Archimedean copulas / Author of the conference Di Bernardino, Elena.
- [Multi angle] Discrete Schur-constant models in inssurance / Author of the conference Lefèvre, Claude.
- [Multi angle] Copulas based inference for discrete or mixed data / Author of the conference Rémillard, Bruno.
- [Multi angle] A measure of dependence for stable distributions / Author of the conference Nolan, John P..
Bibliography
- Biard, R., & Saussereau, B. (2014). Fractional Poisson process: long-range dependence and applications in ruin theory. Journal of Applied Probability, 51(3), 727-740 - http://dx.doi.org/10.1239/jap/1409932670
