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

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

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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 earthquakesOccur along plate boundaries

#1 Chile, 1960M9.5

#2 Alaska, 1964 M9.2

#3 Sumatra, 2004M9.2

#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 theregional 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 betranslated 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 signalswith two different wavelengths

• A position on the earth can be locatedby recording and processing signalsfrom three satellites with known orbits

• Relative locations of stations are usedfor 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 MotionIntensity

BuildingCapacity

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.