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Author
Boratyńska Agata (Warsaw School of Economics, Poland)
Title
Robust Bayesian Insurance Premium in a Collective Risk Model with Distorted Priors under the Generalised Bregman Loss
Source
Statistics in Transition, 2021, vol. 22, nr 3, s. 123-140, tab., wykr., bibliogr. 25 poz.
Keyword
Składki ubezpieczeniowe, Ryzyko, Roszczenia
Insurance premium, Risk, Claims
Note
summ.
Abstract
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 square-error, 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.(original abstract)
Accessibility
The Main Library of the Cracow University of Economics
The Library of Warsaw School of Economics
The Library of University of Economics in Katowice
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Bibliography
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ISSN
1234-7655
Language
eng
URI / DOI
http://dx.doi.org/10.21307/stattrans-2021-030
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