A survey of some recent results on Risk Theory

Florin Avram (florin.avram@univ-pau.fr), Romain Biard (romain.biard@univ-fcomte.fr), Christophe Dutang (dutangc@gmail.com), Stéphane Loisel and Landy Rabehasaina (lrabehas@univ-fcomte.fr)
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Florin Avram: LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau] - UPPA - Université de Pau et des Pays de l'Adour - CNRS - Centre National de la Recherche Scientifique
Romain Biard: LMB - Laboratoire de Mathématiques de Besançon (UMR 6623) - CNRS - Centre National de la Recherche Scientifique - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE]
Christophe Dutang: LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon
Landy Rabehasaina: LMB - Laboratoire de Mathématiques de Besançon (UMR 6623) - CNRS - Centre National de la Recherche Scientifique - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE]

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Abstract: The goal of this paper is to give recent results in risk theory presented at the Conference "Journée MAS 2012" which took place in Clermont Ferrand. After a brief state of the art on ruin theory, we explore some particular aspects and recent results. One presents matrix exponential approximations of the ruin probability. Then we present asymptotics of the ruin probability based on mixing properties of the claims distribution. Finally, the multivariate case, motivated by reinsurance, is presented and some contemporary results (closed forms and asymptotics) are given.

Date: 2014-01
Note: View the original document on HAL open archive server: https://hal.science/hal-01616178v1
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Published in ESAIM: Proceedings, 2014, 44, pp.322 - 337. ⟨10.1051/proc/201444020⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01616178

DOI: 10.1051/proc/201444020

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