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
Englisch

Bibliographic citation
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

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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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