Collective risk modelling for understanding the correlation between multi-peril accumulated losses

Abstract. Hazards such as storms can create multiple perils, such as windstorms and floods, that have correlated annual losses. To better understand the drivers of such correlations, this study explores three collective risk frameworks with varying complexity.

Mathematical expressions are derived explaining how this correlation depends on parameters such as event dispersion (clustering), and the joint distribution of the two hazard variables. Hazard variables are first assumed independent, inducing a positive correlation due to the shared positive dependence on the total number of events. The next framework allows for correlation between the hazard variables, which can then capture negative correlation between accumulated losses. The final framework builds on this by allowing for between-year correlation caused by interannual modulation of the hazard variables.

These frameworks are illustrated using European windstorm gust speeds and precipitation reanalyses from 1980–2000. They are used to diagnose why the correlation between annual wind and precipitation severity indices decreases as thresholds are increased. Only the framework with interannual modulation of the hazard variables quantitatively captures the negative correlations over Europe at high threshold. We propose that one plausible driver for the modulation is the transit time that storms spend near locations.