[Statlist] Séminaires de Statistique

[KONDYLIS Atanassios]

Séminaires de Statistique 

Mardi 22-02-2005 - 11h 00 
Groupe de Statistique, Espace de l'Europe 4, Neuchâtel

PD Dr. Riccardo Gatto 
Universität Bern, Switzerland 
Institut für mathematische Statistik und Versicherungslehre 
riccardo.gatto at stat.unibe.ch


AN ACCURATE ASYMPTOTIC APPROXIMATION FOR EXPERIENCE RATED PREMIUMS

In the Bayesian approach, the experience rated premium is the value which minimizes an expected loss with respect to 
a posterior distribution. The posterior distribution is conditioned on the claim experience of the risk insured, represented 
by a n-tuple of observations. An exact analytical calculation for the experience rated premium is possible under restrictive
circumstances only, regarding the prior distribution, the likelihood function, and the loss function. In this article we provide 
an analytical asymptotic approximation as n goes to infinity for the experience rated premium. This approximation can be 
obtained under more general circumstances, it is simple to compute, and it inherits the good accuracy of the Laplace 
approximation on which it is based. In contrast with numerical methods, this approximation allows for analytical 
interpretations. When exact calculations are possible, some analytical comparisons confirm the good accuracy of this 
approximation, which can even lead to the exact experience rated premium.