Exact and asymptotic results for insurance risk models with surplus-dependent premiums

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Etat: Serval
Version: de l'auteur
ID Serval
serval:BIB_94AD2C27B90A
Type
Article: article d'un périodique ou d'un magazine.
Collection
Publications
Titre
Exact and asymptotic results for insurance risk models with surplus-dependent premiums
Périodique
SIAM Journal of Applied Mathematics
Auteur(s)
Albrecher H., Constantinescu C., Palmowski Z., Regensburger M., Rosenkranz M.
ISSN
0036-1399
Statut éditorial
Publié
Date de publication
2013
Peer-reviewed
Oui
Volume
73
Numéro
1
Pages
47-66
Langue
anglais
Résumé
In this paper we develop a symbolic technique to obtain asymptotic expressions for ruin probabilities and discounted penalty functions in renewal insurance risk models when the premium income depends on the present surplus of the insurance portfolio. The analysis is based on boundary problems for linear ordinary differential equations with variable coefficients. The algebraic structure of the Green's operators allows us to develop an intuitive way of tackling the asymptotic behavior of the solutions, leading to exponential-type expansions and Cramer-type asymptotics. Furthermore, we obtain closed-form solutions for more specific cases of premium functions in the compound Poisson risk model.
Mots-clé
Renewal risk models, Surplus dependent premiums, Boundary value problems, Green's operators, Asymptotic expansions
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Création de la notice
13/09/2012 21:45
Dernière modification de la notice
03/03/2018 19:38
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