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
This object is provided by:
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. If you have any questions about the object, please contact the 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
Other Objects (12)
INFORMATIVE VERSUS NON-INFORMATIVE PRIOR DISTRIBUTIONS AND THEIR IMPACT ON THE ACCURACY OF BAYESIAN INFERENCE
Modelling the occupational and educational choices of young people in Poland using Bayesian multinomial logit models
BAYESIAN MODEL AVERAGING AND JOINTNESS MEASURES: THEORETICAL FRAMEWORK AND APPLICATION TO THE GRAVITY MODEL OF TRADE
THE APPLICATION OF BŰHLMANN-STRAUB MODEL TO THE ESTIMATION OF NET PREMIUM RATES DEPENDING ON THE AGE OF THE INSURED IN THE MOTOR THIRD LIABILITY INSURANCE
BAYESIAN INFERENCE FOR STATE SPACE MODEL WITH PANEL DATA
A Bayesian Small Area Model with Dirichlet Processes on the Responses
MODIFIED RECURSIVE BAYESIAN ALGORITHM FOR ESTIMATING TIME-VARYING PARAMETERS IN DYNAMIC LINEAR MODELS
BAYESIAN SPATIAL ANALYSIS OF CHRONIC DISEASES IN ELDERLY CHINESE PEOPLE USING A STAR MODEL
Change-point detection in CO2 emission-energy consumption nexus using a recursive Bayesian estimation approach
A general Bayesian approach to meet different inferential goals in poverty research for small areas
Comparing particulate matter dispersion in Thailand using the Bayesian Confidence Intervals for ratio of coefficients of variation
Generalised Odd Frechet Family of Distributions: Properties and Applications
INFORMATIVE VERSUS NON-INFORMATIVE PRIOR DISTRIBUTIONS AND THEIR IMPACT ON THE ACCURACY OF BAYESIAN INFERENCE
Modelling the occupational and educational choices of young people in Poland using Bayesian multinomial logit models
BAYESIAN MODEL AVERAGING AND JOINTNESS MEASURES: THEORETICAL FRAMEWORK AND APPLICATION TO THE GRAVITY MODEL OF TRADE
THE APPLICATION OF BŰHLMANN-STRAUB MODEL TO THE ESTIMATION OF NET PREMIUM RATES DEPENDING ON THE AGE OF THE INSURED IN THE MOTOR THIRD LIABILITY INSURANCE
BAYESIAN INFERENCE FOR STATE SPACE MODEL WITH PANEL DATA
A Bayesian Small Area Model with Dirichlet Processes on the Responses
MODIFIED RECURSIVE BAYESIAN ALGORITHM FOR ESTIMATING TIME-VARYING PARAMETERS IN DYNAMIC LINEAR MODELS
BAYESIAN SPATIAL ANALYSIS OF CHRONIC DISEASES IN ELDERLY CHINESE PEOPLE USING A STAR MODEL
Change-point detection in CO2 emission-energy consumption nexus using a recursive Bayesian estimation approach
A general Bayesian approach to meet different inferential goals in poverty research for small areas
Comparing particulate matter dispersion in Thailand using the Bayesian Confidence Intervals for ratio of coefficients of variation
Generalised Odd Frechet Family of Distributions: Properties and Applications
INFORMATIVE VERSUS NON-INFORMATIVE PRIOR DISTRIBUTIONS AND THEIR IMPACT ON THE ACCURACY OF BAYESIAN INFERENCE
Modelling the occupational and educational choices of young people in Poland using Bayesian multinomial logit models
BAYESIAN MODEL AVERAGING AND JOINTNESS MEASURES: THEORETICAL FRAMEWORK AND APPLICATION TO THE GRAVITY MODEL OF TRADE
THE APPLICATION OF BŰHLMANN-STRAUB MODEL TO THE ESTIMATION OF NET PREMIUM RATES DEPENDING ON THE AGE OF THE INSURED IN THE MOTOR THIRD LIABILITY INSURANCE
BAYESIAN INFERENCE FOR STATE SPACE MODEL WITH PANEL DATA
A Bayesian Small Area Model with Dirichlet Processes on the Responses
MODIFIED RECURSIVE BAYESIAN ALGORITHM FOR ESTIMATING TIME-VARYING PARAMETERS IN DYNAMIC LINEAR MODELS
BAYESIAN SPATIAL ANALYSIS OF CHRONIC DISEASES IN ELDERLY CHINESE PEOPLE USING A STAR MODEL
Change-point detection in CO2 emission-energy consumption nexus using a recursive Bayesian estimation approach
A general Bayesian approach to meet different inferential goals in poverty research for small areas
Comparing particulate matter dispersion in Thailand using the Bayesian Confidence Intervals for ratio of coefficients of variation