Risk theory for the compound Poisson process that is perturbed by diffusion

Détails

ID Serval
serval:BIB_98737F70AC6B
Type
Article: article d'un périodique ou d'un magazine.
Collection
Publications
Institution
Titre
Risk theory for the compound Poisson process that is perturbed by diffusion
Périodique
Insurance: Mathematics and Economics
Auteur⸱e⸱s
Dufresne F., Gerber H.U.
ISSN
0167-6687
Statut éditorial
Publié
Date de publication
1991
Peer-reviewed
Oui
Volume
10
Numéro
1
Pages
51-59
Langue
anglais
Résumé
The classical model of collective risk theory is extended in that a diffusion process is added to the compound Poisson process. It is shown that the probabilities of ruin (by oscillation or by a claim) satisfy certain defective renewal equations. The convolution formula for the probability of ruin is derived and interpreted in terms of the record highs of the aggregate loss process. If the distribution of the individual claim amounts are combinations of exponentials, the probabilities of ruin can be calculated in a transparent fashion. Finally, the role of the adjustment coefficient (for example, for the asymptotic formulas) is explained.
Mots-clé
Ruin theory, Risk theory, Renewal equation, Convolution formula, Diffusion, Combinations of exponential claim amounts
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Création de la notice
19/11/2007 10:41
Dernière modification de la notice
20/08/2019 15:00
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