Model Averaging and Grid Maps for Modeling Heavy-Tailed Insurance Data

This work presents a practical approach to improve risk quantification for heavy-tailed insurance claims through model averaging and grid map visualization, addressing the drawbacks of traditional single “best” model selection commonly used in actuarial and model-fitting literature. This is a data-driven study with a focus on Danish fire loss data, where the following are fitted: (i) 16 standard single distributions, (ii) 256 composite distributions, and (iii) 256 mixture distributions; wherein, for the composite and mixture distributions, we focus on the top 20 leading models in terms of the information criterion (i.e., Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC)). Model selection uncertainty is explicitly addressed by AIC and BIC weighted averaging within the Occam’s window (relying on weighted point estimates), while grid maps simultaneously plot information criteria against risk measures, specifically the Value-at-Risk (VaR) and Tail Value-at-Risk (TVaR) at 95% and 99% thresholds, to highlight critical-fit versus tail-risk trade-offs. It is observed that the model-averaged risk measures from composite models align more closely with the empirical values. That is, model-averaged estimates across all categories align closely with empirical VaR0.95 but conservatively elevate TVaR0.99, promoting safer capital reserves. Grid maps and model averaging confirm that mixture and composite models better capture the heavy-tailed nature of Danish fire claims data as compared to fitting a single distribution.