Optimal dividend strategies for two collaborating insurance companies
Détails
Etat: Public
Version: de l'auteur⸱e
ID Serval
serval:BIB_633F4A9ACA56
Type
Article: article d'un périodique ou d'un magazine.
Collection
Publications
Institution
Titre
Optimal dividend strategies for two collaborating insurance companies
Périodique
Advances in Applied Probability
ISSN
0001-8678
1475-6064
1475-6064
Statut éditorial
Publié
Date de publication
06/2017
Peer-reviewed
Oui
Volume
49
Numéro
02
Pages
515-548
Langue
anglais
Résumé
We consider a two-dimensional optimal dividend problem in the context of two insurance companies with compound Poisson surplus processes, who collaborate by paying each other's deficit when possible. We solve the stochastic control problem of maximizing the weighted sum of expected discounted dividend payments (among all admissible dividend strategies) until ruin of both companies, by extending results of univariate optimal control theory. In the case that the dividends paid by the two companies are equally weighted, the value function of this problem compares favorably with the one of merging the two companies completely. We identify this optimal value function as the smallest viscosity supersolution of the respective Hamilton-Jacobi-Bellman equation and provide an iterative approach to approximate it numerically. Curve strategies are identified as the natural analogue of barrier strategies in this two-dimensional context. A numerical example is given for which such a curve strategy is indeed optimal among all admissible dividend strategies, and for which this collaboration mechanism also outperforms the suitably weighted optimal dividend strategies of the two stand-alone companies.
Mots-clé
Statistics and Probability, Applied Mathematics
Web of science
Création de la notice
24/11/2016 12:05
Dernière modification de la notice
20/08/2019 15:19