On total claim amount for marked Poisson cluster models

Abstract : We study the asymptotic distribution of the total claim amount for marked Poisson cluster models. The marks determine the size and other characteristics of the individual claims and potentially influence arrival rate of the future claims. We find sufficient conditions under which the total claim amount satisfies the central limit theorem or alternatively tends in distribution to an infinite variance stable random variable. We discuss several Poisson cluster models in detail, paying special attention to the marked Hawkes processes as our key example.
Type de document :
Article dans une revue
Journal of Applied Probability, Applied Probability Trust, In press
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01788339
Contributeur : Olivier Wintenberger <>
Soumis le : jeudi 21 mars 2019 - 09:16:57
Dernière modification le : mardi 26 mars 2019 - 08:38:31

Fichiers

HawkesCLTFinal.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01788339, version 2
  • ARXIV : 1903.09387

Citation

Bojan Basrak, Olivier Wintenberger, Petra Zugec. On total claim amount for marked Poisson cluster models. Journal of Applied Probability, Applied Probability Trust, In press. 〈hal-01788339v2〉

Partager

Métriques

Téléchargements de fichiers

1