A Simple Method to Study Sensitivity of BMP's |
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Authors: | E. Gómez-Déniz E. Calderín-Ojeda I. Cabrera-Ortega |
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Affiliation: | 1. Department of Quantitative Methods , University of Las Palmas de Gran Canaria , Spain egomez@dmc.ulpgc.es;3. Department of Quantitative Methods , University of Las Palmas de Gran Canaria , Spain;4. Department of Mathematics , University of Las Palmas de Gran Canaria , Spain |
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Abstract: | In this article we measure the local or infinitesimal sensitivity of a kind of Bayes estimates which appear in bonus–malus systems. Bonus–malus premiums can be viewed as a functional depending on the prior distribution. To measure when small changes in the prior cause large changes in the premium we compute the norm of the Fréchet derivative and propose a simple procedure to decide if a bonus–malus premium is robust. As an application, an example where the risk has a Poisson distribution and its parameter follows a Gamma prior distribution is presented under the net and variance premium principles. |
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Keywords: | Bayesian robustness Bonus–malus premium Fréchet Norm |
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