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
case of extreme features of the data. Empirical illustrations on insurance
and operational losses illustrate these findings