Thomas Rauber: Parameter risk in reinsurance

Adviser: Prof. Dr. Peter Bühlmann

July 2009

Abstract:

In this thesis we consider parameter uncertainty that comes along in different
pricing areas in a reinsurance. By parameter risk we mean the risk
of not estimating the parameter properly. We mainly look at parameter risk
in the severity distribution. We differentiate three different ways of
characterising uncertainty. We first replace the parameter that has to be
estimated by a random
variable and derive some analytical result. Then we look into Maximum
Likelihood Estimators and use the result that they are asymptotic normally
distributed. For some examples these asymptotic results are not accurate
enough. Considering these cases we will classify the uncertainty by using
bootstrap. Finally we will specify where uncertainty arises in the
Experience, Exposure and Credibility Rating in praxis. We will see an
example of Credibility Rating which blends Experience and Exposure Rating
by minimizing the parameter risk. 

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