Civil Engineering Reference
In-Depth Information
the coeffi cient of variation of 0.3. The (mean) unit replacement costs are
estimated based on FEMA and NIBS (2003), and do not necessarily refl ect
market/taxation values.
Finally, seismic loss estimation can be conducted based on Monte Carlo
simulation to obtain samples of annual aggregate seismic loss
L
A
for all
buildings and for all seismic events included in the synthetic earthquake
catalogue. Specifi cally,
L
A
is calculated by:
n
m
n
m
A
A
∑
∑
∑
=
∑
[
]
()
=
(
+
(
+
()
L
=
L
δ
L
δ
L
δ
L
δ
,
[28.14]
()
A
EQ
i
ik
RR
ik
CO
ik
BI
ik
k
=
1
i
=
1
k
1
i
=
1
where
n
A
is the number of earthquakes in a year;
m
is the number of build-
ings in the portfolio; and
L
EQ(
i
)
(d
ik
) is the seismic loss to the
i
th property in
the portfolio due to the
k
th event. For simplicity, seismic damage is consid-
ered to be repaired immediately after a seismic event. The generated seismic
loss samples can be used to construct the probability distribution of
L
A
(i.e.
seismic loss curve) and to identify signifi cant scenario events through deag-
gregation analysis (Panel 5 in Fig. 28.1). Moreover, by applying an insurance
policy, seismic loss samples incurred by an insurer can be obtained as
follows:
n
m
n
m
A
A
∑
=
∑
[
]
=
=
∑
i
()
{
(
+
(
+
(()
}
L
=
I
L
δ
I
L
δ
L
δ
L
δ
,
[28.15]
()
A,I
P
EQ
i
ik
P
RR
ik
CO
ik
BI
ik
k
1
i
=
1
k
1
=
1
where
I
P
(•) is the insurance pay-out function and is given by:
LD
LDDLC
CD
0
≤
⎧
⎨
()
EQ
i
⎪
(
)
=
(
)
IL
γ
−
<
<
,
[28.16]
()
()
()
P
Q
i
EQ
i
EQ
i
⎪
(
)
γ
−
L
≥
C
()
EQ
i
in which
D
,
C
and
are the deductible, cap, and coinsurance factor, respec-
tively. The parameters can be adjusted to design various kinds of insurance
pay-out structures to transfer undesirable portions of the probability distri-
bution of seismic loss per property to the insurer. Using Equation [28.15],
the seismic risk exposure curve for an insurer can be developed.
γ
28.4
Earthquake insurance portfolio analysis
28.4.1 Building portfolios of wood-frame houses
in Vancouver
To generate seismic loss samples from the earthquake-engineering-based
model described in Section 28.3, a hypothetical but realistic portfolio of
conventional wood-frame houses in south-western British Columbia is con-
structed. The portfolio includes 2400 wood-frame houses and is divided into
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