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2021 | 22 | nr 3 | 123--140
Tytuł artykułu

Robust Bayesian Insurance Premium in a Collective Risk Model with Distorted Priors under the Generalised Bregman Loss

Warianty tytułu
Języki publikacji
EN
Abstrakty
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 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)
Słowa kluczowe
Rocznik
Tom
22
Numer
Strony
123--140
Opis fizyczny
Twórcy
  • Warsaw School of Economics, Poland
Bibliografia
  • Arias-Nicolás, J. P., Ruggeri, F., Suárez-Llorens, A., (2016). New Classes of Priors Based on Stochastic Orders and Distortion Functions, Bayesian Analysis, Vol. 11, pp. 1107-1136.
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  • Boratyńska, A., (2017). Robust Bayesian estimation and prediction of reserves in exponential model with quadratic variance function, Insurance Math. Econom., Vol. 76, pp. 135-140.
  • Chan, J., Choy, B., Makov, U., (2008). Robust Bayesian analysis of loss reserves data using the generalized t-distribution, ASTIN Bull., Vol. 38, pp. 207-230.
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  • Gómez-Déniz, E., (2009). Some Bayesian Credibility Premiums Obtained by Using Posterior Regret Γ-Minimax Methodology, Bayesian Analysis, Vol. 4, pp. 223-242.
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  • Ruggeri, F., Sánchez-Sánchez, M., Sordo, M.A., Suárez-Llorens, A., (2021). On a New Class of Multivariate Prior Distributions: Theory and Application in Reliability, Bayesian Analysis, Vol. 16, pp. 31-60.
  • Sánchez-Sánchez, M., Sordo, M. A., Suárez-Llorens, A., Gómez-Déniz, E., (2019). Deriving robust Bayesian premiums under bands of prior distributions with applications, ASTIN Bull., Vol. 49, pp. 147-168.
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000171660876

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