Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-22T09:37:00.208Z Has data issue: false hasContentIssue false
  • English
  • Français

ON THE AGGREGATION OF EXPERTS' INFORMATION IN BONUS–MALUS SYSTEMS

Published online by Cambridge University Press:  10 August 2017

Víctor Blanco  and
José M. Pérez-Sánchez
Víctor Blanco*
Affiliation:
Department of Quantitative Methods for Economics & Business, Universidad de Granada, 18011 Granada, Spain
José M. Pérez-Sánchez
Affiliation:
Department of Quantitative Methods for Economics & Business, Universidad de Granada, 18011 Granada, Spain E-Mail: [email protected]
*
E-Mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we propose a new family of premium calculation principles based on the use of prior information from different sources. Under this framework and based on the use of Ordered Weighted Averaging operators, we provide alternative collective and Bayes premiums and describe some approaches to efficiently compute them. Several examples are detailed to illustrate the performance of the new methods.

Keywords

Non-life insurancepremium calculation principlesOrdered Weighted Averagingmathematical programmingBayesian statistics
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 48 , Issue 1 , January 2018 , pp. 311 - 337
Copyright
Copyright © Astin Bulletin 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arbenz, P. and Canestraro, D. (2012) Estimating copulas for insurance from scarce observations, expert opinion and prior information: A Bayesian approach. ASTIN Bulletin, 42 (1), 271–290.Google Scholar
Bacharach, M. (1975) Group decisions in the face of differences of opinion. Management Science, 22, 182–191.Google Scholar
Belles-Sampera, J., Merigó, J.M., Guillén, M. and Santolino, M. (2013) The connection between distortion risk measures and ordered weighted averaging operators. Insurance: Mathematics and Economics, 52, 411–420.Google Scholar
Berger, J. (1985) Statistical Decision Theory and Bayesian Analysis, 2nd edition. New York: Springer-Verlag.CrossRefGoogle Scholar
Blanco, V., El–Haj Ben-Ali, S. and Puerto, J. (2012) Minimizing ordered weighted averaging of rational functions with applications to Continuous Location. Computers & Operations Research, 40, 1448–1460.CrossRefGoogle Scholar
Blanco, V., Puerto, J. and El–Haj, Ben–Ali S. (2014) Revisiting several problems and algorithms in continuous location with ℓτ norms. Computational Optimization and Applications, 58 (3), 563–595.CrossRefGoogle Scholar
Blanco, V., Puerto, J. and Salmerón, R. (2016) A general framework for locating hyperplanes to fitting set of points. Working Paper, available at: http://arxiv.org/abs/1505.03451.Google Scholar
Boucher, J.P., Denuit, M. and Guillen, M. (2009) Number of accidents or number of claims? An approach with zero–inflated poisson models for panel data. Journal of Risk and Insurance, 76 (4), 821–846.Google Scholar
Cardin, M. (2014) A note on natural risk statistics, OWA operators and generalized gini functions. In Mathematical and Statistical Methods for Actuarial Sciences and Finance (eds. Perna, C. and Sibillo, M.), pp. 57–60. Venezia: Springer.Google Scholar
Carretero, R. and Sarabia, A. (2000) Bonus–Malus system in the fuzzy set theory. IEEE International Conference on Fuzzy Systems, 2, 1033–1036.Google Scholar
Casanovas, M., Torres–Martínez, A. and Merigó, J.M. (2015) Decision-making processes of non-life insurance pricing using fuzzy logic and OWA operators. Economic Computation and Economic Cybernetics Studies and Research, 49 (2), 169–187.Google Scholar
Clemen, R.T. and Winkler, R. (1999) Combining probability distributions from experts in risk analysis. Risk Analysis, 19 (2), 187–203.Google Scholar
Emrouznejad, A. and Marra, M. (2014) Ordered weighted averaging operators 1988–2014: A citation-based literature survey. International Journal of Intelligent Systems, 29 (11), 994–1014.Google Scholar
Fernández, E., Pozo, M.A. and Puerto, J. (2014) Ordered weighted average combinatorial optimization: Formulations and their properties. Discrete Applied Mathematics, 169, 97–118.CrossRefGoogle Scholar
Genest, C. and Zidek, J.V. (1986) Combining probability distributions: A critique and an annotated bibliography. Statistical Science, 1 (1), 114–148.Google Scholar
Gerber, H. (1979) An Introduction to Mathematical Risk Theory. Philadelphia: Huebner Foundation.Google Scholar
Gómez, E., Hernández, A., Pérez, J.M. and Vázquez–Polo, F.J. (2002) Measuring sensitivity in a Bonus–Malus system. Insurance: Mathematics & Economics, 31, 105–113.Google Scholar
Gómez–Déniz, E., Vázquez–Polo, F.J. and Pérez, J.M. (2006) A note on computing Bonus–Malus insurance premiums using a hierarchical Bayesian framework. TEST, 15 (2), 345–359.Google Scholar
Gupta, A. and Li, L. (2007) Integrating long-term care insurance purchase decisions with saving and investment for retirement. Insurance: Mathematics and Economics, 41 (3), 362–381.Google Scholar
Gurobi Optimization, Inc. (2015) Gurobi Optimizer Reference Manual. Available at: www.gurobi.com.Google Scholar
Heilmann, W. (1989) Decision theoretic foundations of credibility theory. Insurance: Mathematics and Economics, 8, 77–95.Google Scholar
Hürlimann, W. (1994) A note on experience rating, reinsurance and premium principles. Insurance: Mathematics and Economics, 14, 197–204.Google Scholar
Klugman, S.A., Panjer, H.H. and Willmot, G.E. (2012) Loss Models: From Data to Decisions, 4th edition. New York: John Wiley and Sons.Google Scholar
Lemaire, J. (1979) How to define a Bonus–Malus system with an exponential utility function. ASTIN Bulletin, 10 (3), 274–282.CrossRefGoogle Scholar
Lemaire, J. (1988) Construction of the new Belgian motor third party tariff structure. ASTIN Bulletin, 18 (1), 99–112.CrossRefGoogle Scholar
Lemaire, J. (1998) Bonus–Malus systems: The European and Asian approach to merit-rating (with discussion). North American Actuarial Journal, 2 (1), 1–22.CrossRefGoogle Scholar
Mert, M. and Saykan, Y. (2005) On a Bonus–Malus system where the claim frequency distribution is geometric and the claim severity distribution is pareto. Hacettepe Journal of Mathematics and Statistics, 34, 75–81.Google Scholar
Morillo, I. and Bermúdez, L. (2003) Bonus–Malus system using an exponential loss function with an Inverse Gaussian distribution. Insurance: Mathematics and Economics, 33 (1), 49–57.Google Scholar
Nickel, S. and Puerto, J. (2005) Location Theory: A Unified Approach. Berlin: Springer.Google Scholar
O'Hagan, A., Buck, C., Daneshkhah, A., Eiser, J., Garthwaite, P., Jenkinson, D., Oakley, J. and Rakow, T. (2006) Uncertain Judgements: Eliciting Experts' Probabilities. London: Wiley.CrossRefGoogle Scholar
Reich, A. (1986) Properties of premium calculation principles. Insurance: Mathematics and Economics, 5, 97–101.Google Scholar
Rufo, M.J. and Pérez, C.J. (2012) A Bayesian approach to aggregate experts' initial information. Electronic Journal of Statistics, 6, 2362–2382.CrossRefGoogle Scholar
Shapiro, A.F. (2004) Fuzzy logic in insurance. Insurance: Mathematics and Economics, 35 (2), 399–424.Google Scholar
Shengwang, M., Wei, Y. and Whitmore, G.A. (1999) Accounting for individual overdispersion in a Bonus–Malus system. ASTIN Bulletin, 29 (2), 327–337.Google Scholar
Stone, M. (1961) The opinion pool. Annals of Mathematical Statistics, 32, 1339–1342.Google Scholar
Yager, R.R. (1988) On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Transactions on Systems, Man and Cybernetics, 18, 183–190.Google Scholar
Young, V. (2004) Premium principles. In Encyclopedia of Actuarial Science (eds. Teugels, J.L. and Sundt, B.). New York: John Wiley.Google Scholar