Seismic risk management of insurance losses using extreme value theory and copula - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 753

28
Seismic risk management of insurance losses
using extreme value theory and copula
K. G O DA , University of Bristol, UK and J. R E N,
Western University, Canada
DOI : 10.1533/9780857098986.5.760
Abstract : Extremely large seismic loss due to a catastrophic earthquake
is a serious concern for risk management of multiple buildings and
infrastructure. In particular, accurate modelling of the upper right tail of
seismic loss distribution is important for insurers and reinsurers. This
study discusses a novel statistical approach for characterising the
probability distribution of seismic loss of an insurance portfolio based on
extreme value theory and copula. Its effectiveness is verifi ed through a
numerical example involving seismic loss estimation of multiple wood-
frame houses in Vancouver, Canada. The proposed approach
demonstrates good modelling capability with respect to the earthquake-
engineering-based model, and is useful for more complex risk
management problems.
Key words : catastrophic earthquake risk, earthquake insurance, extreme
value theory, copula, seismic loss dependence.
28.1 Introduction
A catastrophic earthquake and its induced event, such as tsunami and fi re,
affect multiple structures and infrastructure simultaneously, causing cata-
strophic seismic loss to urban cities and coastal towns/communities. Incurred
seismic damage includes loss of life and limb, direct fi nancial loss to building
properties and lifeline facilities, and indirect loss due to the ripple effects
across regional and national economies. The 11 March 2011 M w 9.0 earth-
quake in Tohoku, Japan, was one of such devastating and tragic events
among recent earthquake disasters around the world (e.g. 2004 Sumatra,
2008 Sichuan, and 2010 Haiti earthquakes). Thus vulnerability assessment
to extremely large earthquakes is a global and urgent problem in active
seismic regions. In particular, catastrophic earthquakes impose tremendous
fi nancial stress on insurers and reinsurers underwriting earthquake insur-
ance policies (Kleindorfer and Kunreuther, 1999; Grace et al. , 2003).
Although earthquake insurance loss is not the major part of natural disaster
loss claims, the potential earthquake-related loss can be extremely high. For
instance, two major earthquakes in 2010, M w 8.8 Chile and M w 7.0 Darfi eld
(New Zealand) earthquakes, caused insurance claims of about 8.0 and 4.4
760