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Activity Number:
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509
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Type:
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Contributed
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Date/Time:
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Thursday, August 2, 2007 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Bayesian Statistical Science
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| Abstract - #310233 |
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Title:
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Bayesian Inference Resistant to Outliers Using Super Heavy-Tailed Distributions for the Calculation of Premiums
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Author(s):
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Alain Desgagne*+ and Jean-François Angers
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Companies:
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University of Québec at Montréal and University of Montréal
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Address:
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CP 8888 Succ Centreville, Montreal, QC, H3C 3P8, Canada
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Keywords:
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Bayesian Inference ; Outlier ; Heavy-Tailed Modeling ; Scale Parameter ; Actuarial Science ; Insurance Premiums
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Abstract:
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We assume that the claims for several risks are conditionally independent random variables given the same scale parameter. The Bayesian predictive distribution of a next claim size is used to estimate the pure premium. Robust procedures to conflicting information (prior or outliers) depend mainly on the tail behavior of the likelihood and prior densities. Simple conditions are established to determine the proportion of observations that can be rejected as outliers. It is shown that the posterior distribution converges in law to the posterior that would be obtained from the reduced sample, excluding the outliers, as they tend to 0 or infinity, at any given rate. We compare the log-normal model with the robust super heavy-tailed (log-Pareto type) distributions model. An example of calculation of a pure premium is given.
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