A DEA analysis of risk, cost, and revenues in insurance

Insurance companies have to take risk and cost into account when pricing car insurance policies that cover the risk of private use of cars. In this paper we use data from 80 000 car insurance policies in order to assess, once risk and cost have been taken into account, the combinations of risk that generate the highest returns for the company under existing pricing practices. We use data envelopment analysis (DEA) and frame the study within an analysis of experiments context. The results of DEA are interpreted in a multivariate statistical analysis context using factor analysis, and property fitting techniques. The impact of risk factors in the efficiency is explored by means of regression analysis with dummy variables. There are consequences for the pricing policy of the company.