Robust Bayesian insurance premium in a collective risk model with distorted priors under the generalised Bregman loss

• Authors: Agata Boratyńska

Abstracts

EN

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.

Keywords

EN

classes of priors; posterior regret; distortion function; Bregman loss; insurance premium

• Publisher: Główny Urząd Statystyczny
• Journal: Statistics in Transition new series
• Year: 2021
• Volume: 22
• Issue: 3
• Pages: 123-140

Contributors

author

Agata Boratyńska

• Warsaw School of Economics SGH, Collegium of Economic Analysis, Institute of Econometrics

• https://orcid.org/0000000173631960

Identifiers

DOI

10.21307/stattrans-2021-030

Biblioteka Nauki

1827546