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A New Class of Bayesian Estimators in Paretian Excess-of-Loss Reinsurance

Published online by Cambridge University Press:  29 August 2014

R.-D. Reiss  and
M. Thomas
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Abstract

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For estimating the shape parameter of Paretian excess claims, certain Bayesian estimators, which are closely related to the Hill estimator, have been suggested in the insurance literature. It turns out that these estimators may have a poor performance – just as the Hill estimator – if a certain location parameter is unequal to zero in the Paretian modeling. In an alternative formulation this means that a scale parameter is unequal to 1. Thus, it suggests itself to add the scale parameter in the modeling and to deal with Bayesian estimators of the shape and scale parameters in a full Paretian model. These estimators will be applied to fire and motor reinsurance data. The performance of these estimators will be illustrated by means of Monte Carlo simulations.

Keywords

Excess claimsFire and motor reinsuranceFull Pareto modelGeneralized Pareto modelBayesian estimatorsHill estimatorMaximum likelihood estimator
Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 29 , Issue 2 , November 1999 , pp. 339 - 349
Copyright
Copyright © International Actuarial Association 1999

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