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Linear goal programming and experience rating

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Abstract

This paper is devoted to the explanation of a new methodology in bonus malus system design, capable of taking into account very well known theoretical conditions like fairness and …nancial equilibrium of the portfolio, in addition to market conditions that could …t the resulting scale of premiums into competitive commercial settings. This is done through the resolution of a classical Bayesian decision problem, by means of minimization of the absolute error instead of the classical quadratic error. It is at this stage that we apply Goal Programming methods, which are linear thanks to the equivalence between the minimization of the absolute error and the minimization of the sum of some deviation variables which have a natural interpretation as rating errors. We show in an example how does the new methodology work. All the linear programs have been solved using the simplex method.

Suggested Citation

  • Antonio José Heras Martínez & José Luis Vilar Zanón & José Antonio Fana & Pilar García Pineda, 2001. "Linear goal programming and experience rating," Documentos de trabajo de la Facultad de Ciencias Económicas y Empresariales 01-17, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales.
  • Handle: RePEc:ucm:doctra:01-17
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    File URL: http://eprints.ucm.es/6739/1/0117.pdf
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    References listed on IDEAS

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    1. Vilar, Jose L., 2000. "Arithmetization of distributions and linear goal programming," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 113-122, August.
    2. J.F. Walhin, 1 & Paris, J., 1999. "Using Mixed Poisson Processes in Connection with Bonus-Malus Systems," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 29(01), pages 81-99, May.
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    Keywords

    Programación lineal; Goal Programming; Simplexmethod; Bonus-malus system; Bayes. scale; Rating error; Bayesian decision.;

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