Quantifying and Understanding the Aggregate Risk of Natural Hazards
Hunter, Alasdair
Date: 22 May 2014
Publisher
University of Exeter
Degree Title
PhD in Mathematics
Abstract
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 ...
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.
Doctoral Theses
Doctoral College
Item views 0
Full item downloads 0