Seismic risk management of insurance losses using extreme value theory and copula - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 776

Table 28.3 Ratio of risk measures VaR and TVaR based on the statistical
models with respect to those based on the earthquake-engineering-based
model for insurance seismic loss samples for Groups 2 and 3

Probability
level

GP model and
normal copula

GP model and
HRT copula Risk measure

Ratio of VaR 0.0010 0.9485 0.9288

0.0005 0.8907 0.8965

0.0002 0.9503 0.9845

0.0001 0.9425 0.9916

Ratio of TVaR 0.0010 0.9676 1.0075

0.0005 1.0468 1.0953

0.0002 1.0402 1.0856

0.0001 1.0770 1.1442

the selected fractile. To investigate the effects of using the fi tted seismic loss
models instead of the earthquake-engineering-based model quantitatively,
ratios of VaR and TVaR based on the fi tted models to those based on the
earthquake-engineering-based model are calculated at four exceedance
probability levels between 0.0001 and 0.001, and the results are summarised
in Table 28.3. Biases of the estimated VaR for the normal and HRT copula
models are typically less than 10% error with respect to the earthquake-
engineering-based model (deemed as reasonable). Inspection of the ratios
for TVaR suggests that the fi tted models have heavier right tail than the
earthquake-engineering-based model (this is more applicable to the HRT
copula case). However, this observation needs to be interpreted carefully,
because the lighter right tail of the earthquake-engineering-based model
(more precisely, gradual decrease of heavy right tail behavior) may be
caused by the limitation of the adopted seismic loss model, such as igno-
rance of the compounding indirect seismic loss (which tends to amplify
seismic loss signifi cantly).
Overall, it is concluded that the developed statistical seismic loss models
achieve satisfactory approximation to the earthquake-engineering-based
model, and can be used for complex insurance portfolio analysis. The use
of the developed statistical models is advantageous, because the computa-
tional burden is only a small fraction of the earthquake-engineering-based
model.

28.5 Conclusions and future trends
Extreme value theory for peak-over-threshold data offers a solid theoreti-
cal basis to characterise seismic losses caused by catastrophic earthquakes.
The close attention on large seismic loss data is particularly important for