Optimal ratcheting of dividends in insurance

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Etat: Public
Version: de l'auteur⸱e
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ID Serval
serval:BIB_08E4654E1E64
Type
Article: article d'un périodique ou d'un magazine.
Collection
Publications
Institution
Titre
Optimal ratcheting of dividends in insurance
Périodique
SIAM Journal on Control and Optimization
Auteur⸱e⸱s
Albrecher H., Azcue P., Muler N.
ISSN
0363-0129
Statut éditorial
Publié
Date de publication
2020
Peer-reviewed
Oui
Volume
58
Numéro
4
Pages
1822-1845
Langue
anglais
Résumé
We address a long-standing open problem in risk theory, namely finding the optimal
strategy to pay out dividends from an insurance surplus process, if the dividends are paid
according to a dividend rate that is not allowed to decrease. The optimality criterion
here is to maximize the expected value of the aggregate discounted dividend payments up
to the time of ruin. In the framework of the classical Cramér-Lundberg risk model, we
solve the corresponding two-dimensional optimal control problem and show that the value
function is the unique viscosity solution of the corresponding Hamilton-Jacobi-Bellman
equation. We also show that the value function can be approximated arbitrarily closely
by ratcheting strategies with only a finite number of possible dividend rates and identify
the free boundary and the optimal strategies in several concrete examples. These implementations
illustrate that the restriction of ratcheting does not lead to a large efficiency
loss when compared to the classical un-constrained optimal dividend strategy.
Création de la notice
18/04/2020 11:34
Dernière modification de la notice
13/07/2020 5:21
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