Estimating large losses in insurance analytics and operational risk using the g-and-h distribution

In this paper, we study the estimation of parameters for g-and-h distributions. These distributions find applications in modeling highly skewed and fat-tailed data, like extreme losses in the banking and insurance sector. We first introduce two estimation methods: a numerical maximum likelihood technique, and an indirect inference approach with a bootstrap weighting scheme. In a realistic simulation study, we show that indirect inference is computationally more efficient and provides better estimates than the maximum likelihood method in the case of extreme features in the data. Empirical illustrations on insurance and operational losses illustrate these findings.