Premium determination with multidimensional Bühlmann-Straub credibility model

Abstract

Every insurance company must certainly be able to fulfill its obligations as a guarantor if there are claims submitted by policy holders or insured in the future. Therefore, premium determination is very important for insurance companies. The premium determined by the insurance company contains a net-premium which is an estimate of claims that will be made during the insurance period. So that the net-premium can be determined properly, the insurance company can use the observations of claims that have been made by policy holders or a risk class by considering claims observations from other policy holders or other risk classes that still have similar risks. One of model that can be used in net-premium calculations is the Bühlmann-Straub credibility model. The more information about claims made by policy holders, the net-premium estimation produced is also getting better, because larger observation objects will provide higher accuracy. In some cases, there are insurance products with claims that are relatively rare, therefore if possible the insurance companies can exchange information either directly or through the association of insurance company. However, the Bühlmann-Straub credibility model only considers the information held by the insurance company itself, so in this paper the multidimensional Bühlmann-Straub credibility model is used to determine premium, so that the net-premium calculations can be done using observations from p sources of information or insurance company. The Multidimensional Bühlmann-Straub credibility model can be formed by generalizing from the one-dimensional Bühlmann-Straub credibility model. The multidimensional Bühlmann-Straub credibility model consists of three parameters which must be estimated, namely μ, S, and T, where these parameters can be estimated nonparametrically.