The density of the ruin time for a renewal-reward process perturbed by a diffusion - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2011

The density of the ruin time for a renewal-reward process perturbed by a diffusion

Résumé

Let $X$ be a mixed process, sum of a brownian motion and a renewal-reward process, and $\tau_{x}$ be the first passage time of a fixed level $x<0$ by $X$. We prove that $\tau_x$ has a density and we give a formula for it. Links with ruin theory are presented. Our result may be computed in classical settings (for a Lévy or Sparre Andersen process) and also in a non markovian context with possible positive and negative jumps. Some numerical applications illustrate the interest of this density formula.
Fichier principal
Vignette du fichier
IME-S-11-00229.pdf (2.28 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00625099 , version 1 (20-09-2011)
hal-00625099 , version 2 (03-04-2012)
hal-00625099 , version 3 (04-04-2012)

Identifiants

  • HAL Id : hal-00625099 , version 1

Citer

Christophette Blanchet-Scalliet, Diana Dorobantu, Didier Rullière. The density of the ruin time for a renewal-reward process perturbed by a diffusion. 2011. ⟨hal-00625099v1⟩

Collections

ICJ
386 Consultations
227 Téléchargements

Partager

Gmail Facebook X LinkedIn More