High order expansions for renewal functions and applications to ruin theory - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue The Annals of Applied Probability Année : 2016

High order expansions for renewal functions and applications to ruin theory

Résumé

A high order expansion of the renewal function is provided under the assumption that the inter-renewal time distribution is light tailed with finite moment generating function g on a neighborhood of 0. This expansion relies on complex analysis and is expressed in terms of the residues of the function 1/(1 − g). Under the assumption that g can be extended into a meromorphic function on the complex plane and some technical conditions , we obtain even an exact expansion of the renewal function. An application to risk theory is given where we consider high order expansion of the ruin probability for the standard compound Poisson risk model. This precises the well known Crámer-Lundberg approximation of the ruin probability when the initial reserve is large.
Fichier principal
Vignette du fichier
Dombry_Rabehasaina_revised_preprint_version.pdf (364.14 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01359834 , version 1 (06-09-2016)
hal-01359834 , version 2 (26-11-2016)

Identifiants

Citer

Clément Dombry, Landy Rabehasaina. High order expansions for renewal functions and applications to ruin theory. The Annals of Applied Probability, 2016. ⟨hal-01359834v2⟩

Relations

96 Consultations
152 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More