Multivariate Bühlmann-Straub credibility model for claim reserving

One of the approaches that is used for claim reserving in insurance companies is credibility theory, which allows claim reserving by combining claim payment data with other information. In this paper, the Bühlmann-Straub credibility model is used. Furthermore, in general, claim reserving in a company is done by calculating the claim reserve in each line of business (LoB) in the company, then the total claim reserve for the company (aggregate reserve) is obtained by adding up the claim reserve in each LoB. Considering the possibility that there is correlation between the existing LoBs, the value of aggregate reserve can actually be less than the sum of the claim reserve in each of the existing LoB. Therefore, research on the claim reserving then evolves by considering claim payment data from various LoBs in a company, or also called claim reserving in multivariate context. In this paper, a research is conducted on the development of multivariate Bühlmann-Straub credibility model for claim reserving along with estimation for model's parameters. The model is used to calculate claim reserve for three LoBs of insurance company in United State, based on the data of claim amount during the period of 2008-2017 that was published by Association of Insurance Commisioners of the United State. It appears that the error of multivariate Bühlmann-Straub credibility model is lower than the error of standard Bühlmann-Straub credibility model.