Artikel
Robust Bayesian insurance premium in a collective risk model with distorted priors under the generalised Bregman loss
The article presents a collective risk model for the insurance claims. The objective is to estimate a premium, which is defined as a functional specified up to unknown parameters. For this purpose, the Bayesian methodology, which combines the prior knowledge about certain unknown parameters with the knowledge in the form of a random sample, has been adopted. The generalised Bregman loss function is considered. In effect, the results can be applied to numerous loss functions, including the square-error, LINEX, weighted squareerror, Brown, entropy loss. Some uncertainty about a prior is assumed by a distorted band class of priors. The range of collective and Bayes premiums is calculated and posterior regret Γ-minimax premium as a robust procedure has been implemented. Two examples are provided to illustrate the issues considered - the first one with an unknown parameter of the Poisson distribution, and the second one with unknown parameters of distributions of the number and severity of claims.
- Language
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Englisch
- Bibliographic citation
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Journal: Statistics in Transition New Series ; ISSN: 2450-0291 ; Volume: 22 ; Year: 2021 ; Issue: 3 ; Pages: 123-140 ; New York: Exeley
- Subject
-
classes of priors
posterior regret
distortion function
Bregman loss
insurance premium
- Event
-
Geistige Schöpfung
- (who)
-
Boratyńska, Agata
- Event
-
Veröffentlichung
- (who)
-
Exeley
- (where)
-
New York
- (when)
-
2021
- DOI
-
doi:10.21307/stattrans-2021-030
- Handle
- Last update
-
10.03.2025, 11:42 AM CET
Data provider
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. If you have any questions about the object, please contact the data provider.
Object type
- Artikel
Associated
- Boratyńska, Agata
- Exeley
Time of origin
- 2021
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