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Catastrophe Modeling Workshop Earthquakes
Casualty Actuarial Society Ratemaking and Product Management Seminar
David Lalonde, FCAS,FCIA,MAAA
Society of Actuaries General Insurance Infographic http://www.soa.org/general-ins/
Cat Modeling http://www.casact.org/community/affiliates/case/0312/Wang.pdf
 First practiced by ancient Chinese and
Babylonian traders, General Insurance, also
known as Property and Casualty, has played a
critical role in the evolution of modern society.
 An immense field continuing to grow in size
and complexity. As increased globalization, and
new economies and volatilities emerge, so do
new opportunities—especially for risk-focused
professionals.
 In the United States about 5,000 quakes strike each year. Since
1900 earthquakes have occurred in 39 states and caused damage in
all 50.
 Insured losses from earthquakes were about $45 million in 2013,
far below 2011’s $54 billion, the highest amount ever recorded,
according to Swiss Re.
 The California Earthquake Authority, the state-run entity that is
the largest provider of earthquake insurance in the U.S., has some
800,000 policies in force in the state. Only about 12 percent of
Californians purchase earthquake coverage.
 In the past, earthquake loss was assessed using a collection of
mass inventory data and was based mostly on experts' opinions.
Today it is estimated using a Damage Ratio (DR), a ratio of the
earthquake damage money amount to the total value of a
building. Another method is the use of HAZUS, a computerized
procedure for loss estimation.
 The insurance industry is vital in the process of increasing societal
resilience, especially in planning for and recovering from low-frequency,
high-severity catastrophic events.
 The Swiss Re’s Economics of Climate Adaptation (ECA) research shows
that transferring risk to insurance markets can be the most cost-effective
alternative to manage residual risk for developing economies that can’t
afford massive investments for low-frequency events.
 Insurance also relieves strain on public budgets when disasters occur,
making communities more resourceful.
 Improvements to infrastructure also need to be recognized in a
standardized way. Insurers and investors have no standardized metric for
assessing the resilience of a community. Creating a common 'resilience
rating' might help create the necessary market conditions for doing so,"
Smith told the audience
 2010 had the most devastating earthquakes in recent times. The
largest quakes in Haiti, Chile and New Zealand claimed well over
200,000 lives, almost exclusively in Haiti, and roughly 50 billion
USD in damage to the economy.
 Actual losses varied substantially across affected regions. In the
case of Chile and New Zealand, the events showed that strict
implementation of building codes does save lives by significantly
reducing building damage. Cat modeling assumptions have been
proved to be accurate in this regard.
 From an insurance perspective, one of the key lessons learned is
that so-called secondary loss agents – such as liquefaction and
tsunamis – are generally undervalued in loss modeling. Business
interruption is another widely underestimated risk, especially for
certain industries such as pulp manufacturers, breweries and
refineries.
Only one regional insurance company survived, offering
company stock in place of cash to settle claims.
Earthquake risk is estimated with the help of seismologists.
Losses are reinsured, spreading the risk globally.
Today
Number of Insurer Insolvencies
0
10
20
30
40
50
60
70
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
Year
NumberofInsolvencies
A few insurers go insolvent every year for different reasons.
Catastrophes are no longer the leading cause of insolvencies.
 A rapid, relative displacement of the rock on either side of a
fracture, or fault, in the interior of the solid earth; the energy
released produces seismic waves that radiate outward in all
directions from the initial point of rupture
Ninety percent of the world's earthquakes
Occur along plate boundaries
#1 Chile, 1960
M9.5
#2 Alaska, 1964 M9.2
#3 Sumatra,
2004
M9.2
#4 Tohoku, Japan,
2011 M9.0
 The magnitude 9.0 2011 Tohoku, Japan, and 2004
Sumatra-Andaman, Indonesia, earthquakes were
black swans1 to many earthquake scientists
because of their unexpectedly large magnitudes.
The devastating tsunamis triggered by each
earthquake killed more than 250,000 people and
caused massive economic losses. With the wake-up
call from these two megaquakes, scientists and
businesses want to know the maximum size
earthquake that can occur in a region so that the
seismic hazard can be better addressed and
businesses can be better prepared.
 Black swan is a metaphor, developed by Nassim Nicholas Taleb in his 2007 book, The Black Swan, to describe
an event that is considered rare and unpredictable, has a massive impact, but is retrospectively predictable.
 Earthquake modeling system
Structure/Building
Vulnerability
Hazard
Financial
Event
Generator
Intensity
Calculator
Damage
Estimation
Insured
Loss
Calculation
Exposure
Information
Policy
Condition
KNOWLEDGE DATA
 How regional tectonics – Historical
and instrumentally impact fault
distribution and activity
 How rupture interactions of
fault segments cascade into
large magnitude earthquakes
 How to model time dependent
fault rupture scenarios
 How earthquake ground
motions propagate through a
region
 What are the mechanisms of
local site amplification
 Historical and
instrumentally recorded
earthquake data
 Active and potentially active
faults identified by
geologists
 Paleoseismic and
paleoliquefaction data
 Regional geodetic data
 Earthquake ground motions
(attenuation equations)
 Shear wave velocity in
shallow soils
U.S. Geological Survey (USGS)
California Geological Survey (CGS)
Southern California Earthquake Center
(SCEC)
Global/regional tectonic and geologic information
– Provides a framework for understanding the dynamics of the
regional seismic activities and spatial distribution of earthquakes
Earthquake catalog data
– Spatial distribution of earthquakes
– Rates of small to medium size earthquakes
Paleoseismic & paleoliquefaction data
– Locations and magnitudes of past earthquakes
– Faults slip rates
– Magnitudes and recurrence intervals of characteristic earthquakes
Regional strain rate (GPS) data
– Rate of regional volumetric stain accumulation that can be
translated to regional earthquake potential
The Gutenberg-Richter (GR) distribution is an empirical
relationship between the frequency and magnitude of
earthquakes.
The cumulative annual frequency of earthquakes
decreases as the magnitude increases
But how do you estimate the frequency of
very large events, when there are so few in
the historical record?
Historical catalog ~ 150 yrs
Paleoseismic ~ 10,000s yrs
Geodetic ~ Current Plate Movement
Figure 1.
Deformation regimes
as defined by
Kreemer et al. (2002):
Subduction (S);
diffuse Oceanic (O);
Ridge-transform (R);
Continental (C). Also
shown are 189
shallow earthquakes
above = 5.66 from the
CMT catalog, 1977-
2009.03, which did not
fall into any of these
regimes. These are
considered intraplate
(I) earthquakes.
Figure 1.
Plotting to GR
Relation
Frequency/magnitude
plot of the 189 shallow
intraplate earthquakes
from Figure 1. Also
shown are 3 tapered
Gutenberg-Richter
model curves (Jackson
and Kagan, 1999; Kagan
and Jackson, 2000). All
models have the same
asymptotic spectral
slope of β = 0.63, but
differ in the choice of
corner magnitude
mc. While the match to
the curve with corner
magnitude of 9 appears
best, it must be noted
that this depends on the
size of the single largest
earthquake.
Figure 2.
 Fault Trenching Reveals Offsets in Rock and Soil Layers;
 Carbon Dating Provides Information on Recurrence Rates
Land Survey Stations in San
Francisco Bay Area
• Each satellite broadcasts radio signals
with two different wavelengths
• A position on the earth can be located
by recording and processing signals
from three satellites with known orbits
• Relative locations of stations are used
for horizontal and vertical land survey
?
 Frequency/magnitude curve of the SHIFT/GSRM
long-term shallow earthquake forecast,
retrospectively compared to the CMT catalog of
1977-2009.03. No single tapered Gutenberg-
Richter model is expected to fit this global
composite of different tectonic regimes. Therefore
a straight-line Gutenberg-Richter model with
spectral slope β = 0.63 is shown for
comparison. Error bars on CMT earthquake
counts are two-sigma sampling errors if and only if
the distribution of earthquake counts follows the
binomial distribution; actual sampling errors are
probably larger due to earthquake clustering.
 For each fault, moment rate calculated using
fault length, fault width, and slip rate
 Magnitudes of the characteristic earthquakes
calculated using fault-length relationships
 Total moment rate released by some
combination of the characteristic and
Gutenberg-Richter type earthquakes
 Rupture location for each earthquake
calculated using its related fault geometry and
incorporating random azimuthal and location
uncertainties
Simulated earthquakes to occur not only directly on known faults, but also, with some probability,
anywhere within the region. The addition of smoothed background seismicity
is designed specifically to recognize the potential for earthquakes to occur
where there has been little or no recorded historical seismic activity.
Smoothed background seismicity allows for earthquakes to
occur where there is no historical record, ensuring full spatial
coverage
Ground Motion
Intensity
Building
Capacity
Damage
Damage is computed by the Capacity Spectrum Method
(CSM) and damage functions.
An earthquake demand spectrum curve characterizes the
demand on various buildings imposed by the earthquake.
A building’s capacity curve correlates lateral displacement of
the building to various levels of earthquake demand.
An intersection of the 2 curves corresponds approximately to
the maximum roof displacement of the building in response
to the earthquake.
A damage function correlates the maximum roof
displacement to the expected mean damage on the building.
1. In general, better seismic code (if enforced correctly)
leads to a significant reduction in vulnerability to
earthquake damage.
2. Of two buildings with equal characteristics, the one
built according to a stricter seismic code is likely to
experience less damage in an earthquake.
3. Special buildings are often required to respect even
stricter seismic requirements. For example fire
stations, hospitals, police stations and all emergency
buildings that need to function during and after an
earthquake event.
2 earthquake damage modeling

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2 earthquake damage modeling

  • 1. Source: Catastrophe Modeling Workshop Earthquakes Casualty Actuarial Society Ratemaking and Product Management Seminar David Lalonde, FCAS,FCIA,MAAA Society of Actuaries General Insurance Infographic http://www.soa.org/general-ins/ Cat Modeling http://www.casact.org/community/affiliates/case/0312/Wang.pdf
  • 2.  First practiced by ancient Chinese and Babylonian traders, General Insurance, also known as Property and Casualty, has played a critical role in the evolution of modern society.  An immense field continuing to grow in size and complexity. As increased globalization, and new economies and volatilities emerge, so do new opportunities—especially for risk-focused professionals.
  • 3.  In the United States about 5,000 quakes strike each year. Since 1900 earthquakes have occurred in 39 states and caused damage in all 50.  Insured losses from earthquakes were about $45 million in 2013, far below 2011’s $54 billion, the highest amount ever recorded, according to Swiss Re.  The California Earthquake Authority, the state-run entity that is the largest provider of earthquake insurance in the U.S., has some 800,000 policies in force in the state. Only about 12 percent of Californians purchase earthquake coverage.  In the past, earthquake loss was assessed using a collection of mass inventory data and was based mostly on experts' opinions. Today it is estimated using a Damage Ratio (DR), a ratio of the earthquake damage money amount to the total value of a building. Another method is the use of HAZUS, a computerized procedure for loss estimation.
  • 4.  The insurance industry is vital in the process of increasing societal resilience, especially in planning for and recovering from low-frequency, high-severity catastrophic events.  The Swiss Re’s Economics of Climate Adaptation (ECA) research shows that transferring risk to insurance markets can be the most cost-effective alternative to manage residual risk for developing economies that can’t afford massive investments for low-frequency events.  Insurance also relieves strain on public budgets when disasters occur, making communities more resourceful.  Improvements to infrastructure also need to be recognized in a standardized way. Insurers and investors have no standardized metric for assessing the resilience of a community. Creating a common 'resilience rating' might help create the necessary market conditions for doing so," Smith told the audience
  • 5.  2010 had the most devastating earthquakes in recent times. The largest quakes in Haiti, Chile and New Zealand claimed well over 200,000 lives, almost exclusively in Haiti, and roughly 50 billion USD in damage to the economy.  Actual losses varied substantially across affected regions. In the case of Chile and New Zealand, the events showed that strict implementation of building codes does save lives by significantly reducing building damage. Cat modeling assumptions have been proved to be accurate in this regard.  From an insurance perspective, one of the key lessons learned is that so-called secondary loss agents – such as liquefaction and tsunamis – are generally undervalued in loss modeling. Business interruption is another widely underestimated risk, especially for certain industries such as pulp manufacturers, breweries and refineries.
  • 6. Only one regional insurance company survived, offering company stock in place of cash to settle claims.
  • 7. Earthquake risk is estimated with the help of seismologists. Losses are reinsured, spreading the risk globally. Today
  • 8. Number of Insurer Insolvencies 0 10 20 30 40 50 60 70 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 Year NumberofInsolvencies A few insurers go insolvent every year for different reasons. Catastrophes are no longer the leading cause of insolvencies.
  • 9.  A rapid, relative displacement of the rock on either side of a fracture, or fault, in the interior of the solid earth; the energy released produces seismic waves that radiate outward in all directions from the initial point of rupture
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  • 11. Ninety percent of the world's earthquakes Occur along plate boundaries
  • 12. #1 Chile, 1960 M9.5 #2 Alaska, 1964 M9.2 #3 Sumatra, 2004 M9.2 #4 Tohoku, Japan, 2011 M9.0
  • 13.  The magnitude 9.0 2011 Tohoku, Japan, and 2004 Sumatra-Andaman, Indonesia, earthquakes were black swans1 to many earthquake scientists because of their unexpectedly large magnitudes. The devastating tsunamis triggered by each earthquake killed more than 250,000 people and caused massive economic losses. With the wake-up call from these two megaquakes, scientists and businesses want to know the maximum size earthquake that can occur in a region so that the seismic hazard can be better addressed and businesses can be better prepared.  Black swan is a metaphor, developed by Nassim Nicholas Taleb in his 2007 book, The Black Swan, to describe an event that is considered rare and unpredictable, has a massive impact, but is retrospectively predictable.
  • 14.  Earthquake modeling system Structure/Building Vulnerability Hazard Financial Event Generator Intensity Calculator Damage Estimation Insured Loss Calculation Exposure Information Policy Condition
  • 15. KNOWLEDGE DATA  How regional tectonics – Historical and instrumentally impact fault distribution and activity  How rupture interactions of fault segments cascade into large magnitude earthquakes  How to model time dependent fault rupture scenarios  How earthquake ground motions propagate through a region  What are the mechanisms of local site amplification  Historical and instrumentally recorded earthquake data  Active and potentially active faults identified by geologists  Paleoseismic and paleoliquefaction data  Regional geodetic data  Earthquake ground motions (attenuation equations)  Shear wave velocity in shallow soils
  • 16. U.S. Geological Survey (USGS) California Geological Survey (CGS) Southern California Earthquake Center (SCEC)
  • 17. Global/regional tectonic and geologic information – Provides a framework for understanding the dynamics of the regional seismic activities and spatial distribution of earthquakes Earthquake catalog data – Spatial distribution of earthquakes – Rates of small to medium size earthquakes Paleoseismic & paleoliquefaction data – Locations and magnitudes of past earthquakes – Faults slip rates – Magnitudes and recurrence intervals of characteristic earthquakes Regional strain rate (GPS) data – Rate of regional volumetric stain accumulation that can be translated to regional earthquake potential
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  • 19. The Gutenberg-Richter (GR) distribution is an empirical relationship between the frequency and magnitude of earthquakes. The cumulative annual frequency of earthquakes decreases as the magnitude increases But how do you estimate the frequency of very large events, when there are so few in the historical record? Historical catalog ~ 150 yrs Paleoseismic ~ 10,000s yrs Geodetic ~ Current Plate Movement
  • 20.
  • 21. Figure 1. Deformation regimes as defined by Kreemer et al. (2002): Subduction (S); diffuse Oceanic (O); Ridge-transform (R); Continental (C). Also shown are 189 shallow earthquakes above = 5.66 from the CMT catalog, 1977- 2009.03, which did not fall into any of these regimes. These are considered intraplate (I) earthquakes. Figure 1.
  • 22. Plotting to GR Relation Frequency/magnitude plot of the 189 shallow intraplate earthquakes from Figure 1. Also shown are 3 tapered Gutenberg-Richter model curves (Jackson and Kagan, 1999; Kagan and Jackson, 2000). All models have the same asymptotic spectral slope of β = 0.63, but differ in the choice of corner magnitude mc. While the match to the curve with corner magnitude of 9 appears best, it must be noted that this depends on the size of the single largest earthquake. Figure 2.
  • 23.  Fault Trenching Reveals Offsets in Rock and Soil Layers;  Carbon Dating Provides Information on Recurrence Rates
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  • 25. Land Survey Stations in San Francisco Bay Area • Each satellite broadcasts radio signals with two different wavelengths • A position on the earth can be located by recording and processing signals from three satellites with known orbits • Relative locations of stations are used for horizontal and vertical land survey
  • 26. ?
  • 27.  Frequency/magnitude curve of the SHIFT/GSRM long-term shallow earthquake forecast, retrospectively compared to the CMT catalog of 1977-2009.03. No single tapered Gutenberg- Richter model is expected to fit this global composite of different tectonic regimes. Therefore a straight-line Gutenberg-Richter model with spectral slope β = 0.63 is shown for comparison. Error bars on CMT earthquake counts are two-sigma sampling errors if and only if the distribution of earthquake counts follows the binomial distribution; actual sampling errors are probably larger due to earthquake clustering.
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  • 29.  For each fault, moment rate calculated using fault length, fault width, and slip rate  Magnitudes of the characteristic earthquakes calculated using fault-length relationships  Total moment rate released by some combination of the characteristic and Gutenberg-Richter type earthquakes  Rupture location for each earthquake calculated using its related fault geometry and incorporating random azimuthal and location uncertainties
  • 30. Simulated earthquakes to occur not only directly on known faults, but also, with some probability, anywhere within the region. The addition of smoothed background seismicity is designed specifically to recognize the potential for earthquakes to occur where there has been little or no recorded historical seismic activity.
  • 31. Smoothed background seismicity allows for earthquakes to occur where there is no historical record, ensuring full spatial coverage
  • 33. Damage is computed by the Capacity Spectrum Method (CSM) and damage functions. An earthquake demand spectrum curve characterizes the demand on various buildings imposed by the earthquake. A building’s capacity curve correlates lateral displacement of the building to various levels of earthquake demand. An intersection of the 2 curves corresponds approximately to the maximum roof displacement of the building in response to the earthquake. A damage function correlates the maximum roof displacement to the expected mean damage on the building.
  • 34. 1. In general, better seismic code (if enforced correctly) leads to a significant reduction in vulnerability to earthquake damage. 2. Of two buildings with equal characteristics, the one built according to a stricter seismic code is likely to experience less damage in an earthquake. 3. Special buildings are often required to respect even stricter seismic requirements. For example fire stations, hospitals, police stations and all emergency buildings that need to function during and after an earthquake event.

Editor's Notes

  1. Most insurance companies were not able to cover the damages caused to policyholders by the 1906 Earthquake. Fireman’s Fund survived by convincing its policyholders to accept shares of stock in the company in place of indemnifying their loss with cash. Policyholders were willing to accept the stock because they knew the company’s equity was inadequate. The stock eventually regained its value. This type of innovative thinking is essential to the success of the insurance industry, still today.
  2. Now earthquake risk is estimated with help from seismologists. Losses are reinsured. Reinsurance is when companies insure other companies for extreme events, and each one shares a small part of the large loss. This allows losses to be spread all over the world, so that no single insurer will be made insolvent by one local event like the 1906 earthquake.
  3. Note that insolvencies in 2001 and 2002 were not very high compared to the 1980’s, despite “unexpected” catastrophic loss from terrorist attacks. Total insolvencies in 1985 and 1982 comprised 2.26% and 2.29% of the companies in the total industry. 2001 was 0.88%. Insurers are much better prepared for catastrophic events today than they were in 1906. This is due to advancements in the industry through innovative thinking.