Robustness in bayesian models for bonus-malus systems

Intelligent And Other Computational Techniques In Insurance: Theory And Applications

Volumn , Issue , 2003, Pages 435-463

  Gómez Déniz, Emilio ^a   Vázquez Polo, Francisco J ^b  

^a Titular de Universidad   (Spain)

^b UNIVERSITY OF LAS PALMAS DE GRAN CANARIA   (Spain)

Author keywords

Bayesian robustness; Bonus malus; Classes of priors; Generalized moments conditions; contamination class

Indexed keywords

EID: 85116520952     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/9789812794246_0012     Document Type: Chapter

References (22)

1. Berger, J. (1985), Statistical Decision Theory and Bayesian Analysis, 2nd edition, Springer-Verlag, New York.
2. Besson, J.L. and Partrat, C. (1992), “Trend et systèmes de bonus-malus, " ASTIN Bulletin, vol. 22, 1, pp. 11-31.
3. Betrò, B., Ruggeri, F. and Mȩczarski, M. (1994), “Robust Bayesian analysis under generalized moments conditions, " Journal of Statistical Planning and Inference, vol. 41, pp. 257-266.
4. Bühlmann, H. (1970), Mathematical methods in Risk theory, Springer-Verlag, Berlin.
5. Cano, J. (1993), “Robustness of the posterior mean in normal hierarchical models, " Commun. Statist. Theory & Meth., vol. 22, 7, pp. 1999-2014.
6. Eichenauer, J., Lehn, J. Retting, S. (1988), “A gamma-minimax result in credibility theory, " Insurance: Mathematics and Economics, vol. 7, 1, pp. 49-57.
7. Frangos, N. and Vrontos, S. (2001), “Design of optimal bonus-malus systems with a frequency and severity component on an individual basis in automobile insurance, " ASTIN Bulletin, vol. 31, 1, pp. 1-22.
8. Gómez, E., Hernández, A. and Vázquez-Polo, F. (2000), “Robust Bayesian premium principles in Actuarial Science, " J. Royal Stat. Soc, Series D, vol. 49, 2, pp. 241-252.
9. Gómez, E., Hernández, A. and Vázquez-Polo, F. (2002a), “Bounds for ratios of posterior expectations: Applications in the collective risk model, " Scandinavian Actuarial Journal, vol. 1, pp. 37-44.
10. Gómez, E., Pérez, J., Hernández, A. and Vázquez-Polo, F. (2002b), “Measuring sensitivity in a bonus-malus system, " Insurance: Mathematics & Economics, vol. 31, 1, pp. 105-113.
11. Goutis, C. (1994), “Ranges of posterior measures for some classes of priors with specified moments, " International Statistical Review, vol. 62, 2, pp. 245-256.
12. Heilmann, W. (1989), “Decision theoretic foundations of credibility theory, " Insurance: Mathematics & Economics, vol. 8, pp. 77-95.
13. Lemaire, J. (1979), “How to define a bonus-malus system with an exponential utility function, " Astin Bulletin, vol. 10, 3, pp. 274-282.
14. Lemaire, J. (1995), Bonus-Malus Systems in automobile insurance, Kluwer Academic Publishers, London.
15. Makov, U. (1995), “Loss robustness via Fisher-weighted squared-error loss function, " Insurance: Mathematics & Economics, vol. 16, pp. 1-6.
16. Meng, Y.W. and Whitmore, G.A. (1999), “Accounting for individual over-dispersion in a bonus-malus automobile insurance system, " Astin Bulletin, vol. 29, 2, pp. 327-337.
17. Ríos-Insúa, D. and Ruggeri, F. (2000), Robust Bayesian Statistics, Springer-Verlag, New York.
18. Scollnik, D. (1996), “An introduction to Markov Chain Monte Carlo methods and their actuarial applications, ", in Proceeding of the Casualty Actuarial Society, LXXXIII, pp. 114-165.
19. Sivaganesan, S. (1991), “Sensitivity of some posterior summaries when the prior is unimodal with specified quantiles, " The Canadian Journal of Statistics, vol. 19, 1, pp. 57-65.
20. Sivaganesan, S. and Berger, J. (1989), “Ranges of posterior measures for priors with unimodal contaminations, " Annals of Statistics, vol. 17, 2, pp. 868-889.
21. Tremblay, L. (1992), “Using the Poisson inverse Gaussian in Bonus-Malus Systems, " Astin Bulletin, vol. 22, 1, pp. 97-106.
22. Winkler, G. (1988), “Extreme points of moment sets, " Mathematics of Operations Research, vol. 13, 4, pp. 581-587.