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Solvency tuned premium for a composite loss distribution

Brouste, Alexandre; Matoussi, Anis; Rohmer, Tom; Dutang, Christophe; Désert, Vanessa; Gales, Erwan; Golhen, Pierre; Milleville, Bérengère; Lekeufack, Willie (2018), Solvency tuned premium for a composite loss distribution. https://basepub.dauphine.fr/handle/123456789/18538

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Generalized_Pareto_2018-07-07.pdf (298.8Kb)
Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-01883508
Date
2018
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Published in
Paris
Pages
17
Metadata
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Author(s)
Brouste, Alexandre cc
Laboratoire Manceau de Mathématiques [LMM]
Matoussi, Anis
Laboratoire Manceau de Mathématiques [LMM]
Rohmer, Tom
Laboratoire Manceau de Mathématiques [LMM]
Dutang, Christophe cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Désert, Vanessa
Laboratoire Manceau de Mathématiques [LMM]
Gales, Erwan

Golhen, Pierre

Milleville, Bérengère

Lekeufack, Willie
Abstract (EN)
A parametric framework is proposed to model both attritional and atypical claims for insurance pricing. This model relies on a classical Generalized Linear Model for attritional claims and a non-standard Generalized Pareto distribution regression model for atypical claims. Maximum likelihood estimators (closed-form for the Generalized Linear Model part and computed with Iterated Weighted Least Square procedure for the Generalized Pareto distribution regression part) are proposed to calibrate the model. Two premium principles (expected value principle and standard deviation principle) are computed on a real data set of fire warranty of a corporate line-of-business. In our methodology, the tuning of the safety loading in the two premium principles is performed to meet a solvency constraint so that the premium caps a high-level quantile of the aggregate annual claim distribution over a reference portfolio.
Subjects / Keywords
commercial lines; non-life insurance; pricing; composite distribution; solvency criterion

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