Abstract credibility |
| |
| Authors: | G. C. Taylor |
| |
| Affiliation: | 1. School of Economic &2. Financial Studies , Macquarie University , North Ryde , N.S.W. , 2113 , Australia |
| |
| Abstract: | Abstract This paper falls into three parts. The first part (Sections 1 to 4) consists of an attempt to consolidate the existing credibility models, which are rapidly becoming more numerous, by constructing one large all-embracing model. In order to do this, it is necessary to abstract from the usual setting of Credibility Theory, the insurance world, and work in more abstract Hilbert spaces. This increases the complexity of the theory, but the results appear nevertheless in a form familiar to credibility theorists. The second part (Section 5) shows that, in the so-called inhomogeneous case of credibility estimation, best estimates are obtained if one uses sufficient statistics, a result which has previously been known under much more restricted circumstances. In the same section it is pointed out that the validity of the analogous result in the homogeneous case is by no means obvious. The third part (Section 6) demonstrates that a number of existing credibility models can be derived as special cases of the model developed here, and goes on to deal briefly with a couple of new models which arise naturally out of the abstract credibility formulation. |
| |
| Keywords: | |
|
|
