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

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  • Boratyńska Agata

    (Warsaw School of Economics SGH, Collegium of Economic Analysis, Institute of Econometrics, Al. Niepodległości 162, 02-554 Warszawa, Poland .)

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.

Suggested Citation

  • Boratyńska Agata, 2021. "Robust Bayesian insurance premium in a collective risk model with distorted priors under the generalised Bregman loss," Statistics in Transition New Series, Statistics Poland, vol. 22(3), pages 123-140, September.
    • Handle: RePEc:vrs:stintr:v:22:y:2021:i:3:p:123-140:n:8
    DOI: 10.21307/stattrans-2021-030
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    References listed on IDEAS

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    1. Lemaire, Jean, 1979. "How to Define a Bonus-Malus System with an Exponential Utility Function," ASTIN Bulletin, Cambridge University Press, vol. 10(3), pages 274-282, December.
    2. Young, Virginia R., 2000. "Credibility using semiparametric models and a loss function with a constancy penalty," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 151-156, May.
    3. James Berger & Elías Moreno & Luis Pericchi & M. Bayarri & José Bernardo & Juan Cano & Julián Horra & Jacinto Martín & David Ríos-Insúa & Bruno Betrò & A. Dasgupta & Paul Gustafson & Larry Wasserman &, 1994. "An overview of robust Bayesian analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 3(1), pages 5-124, June.
    4. Furman, Edward & Zitikis, Ricardas, 2008. "Weighted premium calculation principles," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 459-465, February.
    5. Alejandro Balbás & José Garrido & Silvia Mayoral, 2009. "Properties of Distortion Risk Measures," Methodology and Computing in Applied Probability, Springer, vol. 11(3), pages 385-399, September.
    6. Chan, Jennifer S.K. & Boris Choy, S.T. & Makov, Udi E., 2008. "Robust Bayesian Analysis of Loss Reserves Data Using the Generalized-t Distribution," ASTIN Bulletin, Cambridge University Press, vol. 38(1), pages 207-230, May.
    7. Ali Karimnezhad & Ahmad Parsian, 2014. "Robust Bayesian methodology with applications in credibility premium derivation and future claim size prediction," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(3), pages 287-303, July.
    8. 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 Bulletin, Cambridge University Press, vol. 49(1), pages 147-168, January.
    9. Heilmann, Wolf-Rudiger, 1989. "Decision theoretic foundations of credibility theory," Insurance: Mathematics and Economics, Elsevier, vol. 8(1), pages 77-95, March.
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