Quantifying and Understanding the Aggregate Risk of Natural Hazards
Thesis or dissertation
University of Exeter
Statistical models are necessary to quantify and understand the risk from natural hazards. A statistical framework is developed here to investigate the e ect of dependence between the frequency and intensity of natural hazards on the aggregate risk. The aggregate risk of a natural hazard is de ned as the sum of the intensities for all events within a season. This framework is applied to a database of extra tropical cyclone tracks from the NCEP-NCAR reanalysis for the October to March extended winters between 1950 and 2003. Large positive correlation is found between cyclone counts and the local mean vorticity over the exit regions of the North Atlantic and North Paci c storm tracks. The aggregate risk is shown to be sensitive to this dependence, especially over Scandinavia. Falsely assuming independence between the frequency and intensity results in large biases in the variance of the aggregate risk. Possible causes for the dependence are investigated by regressing winter cyclone counts and local mean vorticity on teleconnection indices with Poisson and linear models. The indices for the Scandinavian pattern, North Atlantic Oscillation and East Atlantic Pattern are able to account for most of the observed positive correlation over the North Atlantic. The sensitivity of extremes of the aggregate risk distribution to the inclusion of clustering, with and without frequency intensity dependence, is investigated using Cantelli bounds and a copula simulation approach. The inclusion of dependence is shown to be necessary to model the clustering of extreme events. The implication of these ndings for the insurance sector is investigated using the loss component of a catastrophe model. A mixture model approach provides a simple and e ective way to incorporate frequency-intensity dependence into the loss model. Including levels of correlation and overdispersion comparable to that observed in the reanalysis data results in an average increase of over 30% in the 200 year return level for the aggregate loss.
Stephenson, David B.
PhD in Mathematics