Modelling auto insurance Size-of-Loss distributions using Exponentiated Weibull distribution and de-grouping methods

Abstract

Rate regulation plays an important role in the financial service of the auto insurance industry. Modelling the Size of Loss distributions, particularly the large loss distribution at the aggregate level, is a key component of rate regulation to produce a benchmark for the industry. However, traditionally actuarial practice is constructing the group-based Size of Loss with irregular intervals. The frequency values associated with each group are counted to form a frequency distribution. However, this approach is limited by lacking a parametric distribution that can capture the underlying randomness of the Size of Loss. In this work, we propose a de-grouping method based on the simulation of the uniform random variate, with and without constraint on knowing the average incurred loss per claim count. Using the de-grouping method, we simulate the individual observation based on the limited information available from the grouped Size of Loss. We have successfully identified the Exponentiated Weibull distribution as a good candidate as it outperforms other heavy-tailed distributions being considered. Our findings provide critical guidance and direction for the practical use of the proposed de-grouping method in auto insurance rate regulation practice and other fields in business and economics.