A survey of some recent results on Risk Theory

Florin Avram (1) , Romain Biard (2) , Christophe Dutang (3) , Stéphane Loisel (3) , Landy Rabehasaina (2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
3 SAF - Laboratoire de Sciences Actuarielle et Financière

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.

Domaines: Applications [stat.AP]; Calcul [stat.CO]; Statistiques [math.ST]; Finance quantitative [q-fin.CP]

Florin Avram, Romain Biard, Christophe Dutang, Stéphane Loisel, Landy Rabehasaina. A survey of some recent results on Risk Theory. ESAIM: Proceedings, 2014, 44, pp.322 - 337. ⟨10.1051/proc/201444020⟩. ⟨hal-01616178⟩