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Quasi-Likelihood Estimation of Benchmark Rates for Excess of Loss Reinsurance Programs

Published online by Cambridge University Press:  09 August 2013

Robert Verlaak ,
Werner Hürlimann  and
Jan Beirlant
Robert Verlaak
Affiliation:
Aon Benfield, Brussels, Faculty of Business and Economics, Katholieke Universiteit Leuven, Belgium, E-mail: robert.verlaak@skynet.be
Werner Hürlimann
Affiliation:
IRIS integrated risk management ag, Zürich, Swiss
Jan Beirlant
Affiliation:
Department of Mathematics and Leuven Statistics Research Centre, Katholieke Universiteit Leuven, Belgium
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Abstract

In this paper a method for determining benchmark rates for the excess of loss reinsurance of a Motor Third Party Liability insurance portfolio will be developed based on observed market rates. The benchmark rates are expressed as a percentage of the expected premium income that is available to cover the whole risk of the portfolio. The rates are assumed to be based on a compound process with a heavy tailed severity, such as Burr or Pareto distributions. In the absence of claim data these assumptions propagate the theoretical benchmark rate component of the regression model.

Given the whole set of excess of loss reinsurance rates in a given market, the unknown parameters are estimated within the framework of quasi-likelihood estimation. This framework makes it possible to select a theoretical benchmark rate model and to choose a parsimonious submodel for describing the observed market rates over a 4-years observation period. This method is applied to the Belgian Motor Third Party Liability excess of loss rates observed during the years 2001 till 2004.

Keywords

Excess-of-loss reinsuranceBurr distributionPareto distributionbenchmark rategeneralised (non-) linear modelsquasi-likelihoodweighted Pearson residuals
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 39 , Issue 2 , November 2009 , pp. 429 - 452
Copyright
Copyright © International Actuarial Association 2009

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