 |
|
|
|
| HAL : hal-00625099, version 3 |
| DOI : 10.1016/j.aml.2012.04.003 |
| Fiche détaillée |  Récupérer au format |
|
|
| Applied Mathematics Letters 26, 1 (2013) http://dx.doi.org/10.1016/j.aml.2012.04.003 |
|
|
| Versions disponibles : | v1 (20-09-2011) | v2 (03-04-2012) | v3 (05-04-2012) |
|
|
|
|
| The density of the ruin time for a renewal-reward process perturbed by a diffusion |
|
|
| Christophette Blanchet-Scalliet 1Diana Dorobantu 2 |
|
|
| (2013) |
|
|
|
| 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. |
|
|
|
|
|
|
|
|
|
|
|
| 1 : | Institut Camille Jordan (ICJ) |
|
|
|
CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon |
|
|
| 2 : | Laboratoire de Sciences Actuarielle et Financière (SAF) |
|
|
|
Université Claude Bernard - Lyon I : EA2429 |
|
|
|
|
|
|
|
|
|
| Domaine | : | Mathématiques/Probabilités Économie et finance quantitative/Gestion des risques |
|
|
| Renewal-reward process – Brownian motion – Jump-diffusion process – Time of ruin. |
|
|
|
| Liste des fichiers attachés à ce document : | |||||
|
|||||
|
|
|
| hal-00625099, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00625099 | |
| oai:hal.archives-ouvertes.fr:hal-00625099 | |
| Contributeur : Didier Rullière | |
| Soumis le : Mercredi 4 Avril 2012, 18:53:10 | |
| Dernière modification le : Vendredi 14 Décembre 2012, 09:29:54 | |
