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CAT MODELING 101:
HURRICANE & EARTHQUAKE
Mark Bove, CPCU, AReSenior Research Meteorolo istMunich Reinsurance America, Inc.
RAA Catastrophe Modeling Conference12 February 2013
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Agenda
Cat Modeling Basics
Model Components
Model Process
Event Set Creation
Intensit Calculation
Vulnerability
Earthquake Modeling Basics
Event Set Creation
Intensity Calculation
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Basic Building Blocks of Catastrophe Models
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Basic Building Blocks of Catastrophe Models
There are four basic components to all catastrophe
models, regardless of the peril being modeled.
oc as c ven e
Dama e Estimation
Loss Evaluation
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Basic Building Blocks of Catastrophe Models
Stochastic Event Set
A set of discrete events covering all the important combinations of location,, ,
the (annual) probability of each event.
Account for all locations that are
impacted by peril of interest.
Have a sufficient number of events to
A Stochastic Event Set
should:
cover all possible sizes and intensities
that are possible in a given location.
Consider the probability of a given event
occurring.
Have enough events to produce
statistically stable loss results.
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Basic Building Blocks of Catastrophe Models
Intensity Calculation
A set of rules to calculate the intensity of each event at every site of interestindividual location insurance ortfolio etc.
Be based on established physics of the
hazard being modeled.
Intensity Calculations
should:
Should be calculated at every location
of interest.
Should consider environmental
influences at or around site of interest.
To calculate event intensities at each location of interest, the model requires
Geocodin and the relevant Geos atial Hazard Databases for the eril bein
modeled. Both of these tools are included in the model.
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Basic Building Blocks of Catastrophe Models
Intensity Calculation
Geocoding
data (building number, street, city, state, and postal code) into coordinates(usually latitude and longitude) that the risk modeling software can process.
,
better.
555 College Road East
Princeton, NJ 08543
= 40.351 N, 74.593 W
Map: Munich Reinsurance America
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Basic Building Blocks of Catastrophe Models
Intensity Calculation
Geospatial Hazard Databases
a a ases con a n ng n orma on
on the local environmental and/or
physical factors that can influence
an even s n ens y a e s e.
The relevant information depends
on the eril; With res ect to tro ical
cyclones: topography and surface
roughness.
Source: USGS
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Basic Building Blocks of Catastrophe Models
Damage Estimation
Computational models to estimate the damage level of each structure, givenits vulnerability to the particular peril and the events intensity at the site
Consider several types of construction and buildingoccupancy (primary modifiers).
Consider other construction techniques that either
Dama e Estimation
ncrease or ecrease vu nera ty to t e per n
question (i.e. secondary modifiers). Consider the initial quality of construction, including
the adoption and enforcement of building codes, aswell as the a e and the maintenance of the buildin .
should: Have different damage/vulnerability functions for
buildings (structural and nonstructural elements),
contents, and time element.
Use a consistent measure to correlate event intensity
.
Account for so-called secondary hazards, such as
storm surge and demand surge.
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Basic Building Blocks of Catastrophe Models
Loss Evalution
Evaluate insured losses, given the damage level & values, as well as thea licable insurance and reinsurance structures, such as deductibles, limits,
Determine how building damage
translates into insurance loss.
attachment points, treaty cessions, etc.
Determine whether or how to account
for:
Demand surgeoss va ua on
should:
Inflated claims
Aggressive construction contractors
Questionable claims settlement
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Basic Building Blocks of Catastrophe Models
Model Output
Losses can be produced for a variety of financial perspectives.
The output of the catastrophe model contains the losses by event by
financial perspective.
Ground Up Loss
(Loss before policy limits/deductibles)
(Loss after application of limits and deductibles)
Treaty Loss
(Loss to individual treaties)Financial perspectives
Net Loss
(Loss after limits, deductibles, and treaties)
Reinsurance loss
(Loss suffered by the reinsurer)
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Basic Building Blocks of Catastrophe Models
Model Flowchart
Provided by user Part of model
Stochastic
Event SetGeocoding
Engine
Intensity
CalculationGeospatialxposure
Data
Damage
Estimation
Database
Insurance Lossruc ure Evaluation
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Basic Building Blocks of Catastrophe Models
Detailed Model Flowchart
1. Stochastic Event Set 2. Intensity Calculation
Let x=1 & n = Number of Events in Set.
If Event x footprint impacts any
location of interest, go to step 2.tensityatSite
int
, .
Complete when all n events are
assessed. EventIn
Source-to-Site Distance
dist
3. Damage Estimation
r
4. Loss Evaluation
sity Deductible
DamageFac
t
mean DF
The standard deviation
is usually estimated as
a function of the mean
robabilityDe
n
Ground-Up Loss= DF x Repl. Value
Limit
Event Intensity at SiteGround-Up Loss
.
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Basic Building Blocks of Catastrophe Models
Model Output
Loss evaluation Event loss tables ELT
Simulated losses are stored for each simulated event and location in an event loss
table (ELT) together with associated occurrence frequencies (probabilities)
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Basic Building Blocks of Catastrophe Models
Model OutputCreating Event Loss Distributions
Combine covera es buildin contents time
element) to arrive at a site (account) loss
distribution for each event .
Involves evaluating
the sum of correlated
random variables and
each event.
Combine policies to produce a portfolio loss
deductibles and limits.
.
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Basic Building Blocks of Catastrophe Models
Model Output
Creating Annual Loss Distributions By evaluating the
Combine all event loss distributions toarrive at an annualized probability
pro a y a e oss
from any one (two, threeetc.) event(s) can exceed
any given threshold..
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Basic Building Blocks of Catastrophe Models
Model Output
Losses can be anal zed and a re ated on a location, olic or ortfolio level for which different
Exceedance Probability (EP) / Probable Maximum Loss (PML) Curve
insurance and / or financial structures can be applied for an event or annual aggregate basis
ce
edanc
PML
bilityofE
AAL
ualProb
Loss ($)
An
N-yr Loss
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Hurricane Modeling Basics
Source: NOAA
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Perils included in U.S. Tropical Cyclone Models
Explicitly Modeled Perils (Perils included in Event Set/Intensity Calculation):
Direct Wind Damage
Wave action (Offshore Platform Only)
Implicitly Modeled Perils (Perils included via vulnerability curves):
Indirect wind damage (Falling trees & limbs, projectiles, etc.)
Thunderstorm-related perils (Lightning, Hail, Tornado)
Wave Action (Mainland US Only) Coastal Erosion
Non-Modeled Perils:
Winter Storm perils occurring in Transitioning Storms
Secondary events triggered by tropical cyclone, such as nuclear plant incidents orprolonged inland flooding.
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Tropical Cyclone Event Set Development
Primary Stochastic Event Set Methodologies
Event Tree
Modeling using every possible intensity at every desired location,
Landfall parameters for stochastic events are fixed for each U.S.
landfall
Basin Simulation
ttempt to mo e t e ent re t ant c as n to recreate rea st churricane event sets using hundreds of thousands of model
iterations (years)
Each stochastic events characteristics are allowed to evolve over
time based on model parameters
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Tropical Cyclone Event Set Development:
Event Tree Example
10 miles m es
Point 1
Intensity
55 mph 75mph 95 mph 115 mph 135 mph 155 mph
45 90 135 45 90 135 45 90 135 45 90 135 45 90 135 45 90 135
Landfall Angle
10m 20m 30m 10m 20m 30m 10m 20m 30m
Rmax
Six intensities * 3 landfall angles * 3 Rmax sizes = 54 Events at Point 1.
Procedure is then repeated at Point 2, Point 3, , Point N.
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Tropical Cyclone Event Set Development:
Basin Simulation
Attempt to model the entire Atlantic Basin to recreate realistichurricane event sets using hundreds of thousands of modelera ons years
statistical data from the historical event database (HURDAT) tocreate realistic simulations of Atlantic activity
Number of overall events er ear & U.S. landfalls eryear
Genesis / Lysis locations
Maximum sustained winds
Central pressure
Radius of maximum winds
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Tropical Cyclone Event Set Development:
Basin Simulation
ModelYear
# Events
hurricane activity for 10,000 years. Using the fitted distribution of Atlantic
1 10
2 17
3 8
activity (previous slide), we can use a
random number generator to determine4 11
5 13
year
Once we determine how man events
7 9
8 12
form in each year, the next question is:Where in the Atlantic did they form?
9 1210 7
11 18
10,000 14
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Tropical Cyclone Event Set Development:
Basin Simulation
Map: Munich Reinsurance America
Model Year 1
Event 8
Event 7
Event 6Event 4
Event 2Event 10
Event 1Event 9
Event 5
s ng e a a ase, one can oca e e po n s o or g n o s or ca
storms in the Atlantic. One can then create a 2D genesis probabili ty field based
on these data, then randomly assign genesis locations based on the 2D field.
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Tropical Cyclone Event Set Development:
Basin Simulation
Storm Movement
Using HURDAT data, one can
Map: NOAA Coastal Services Center
ca cu a e s a s cs on ra e o s orm
motion and storm direction Tropical cyclone speed and direction
,one cant use statistics from theentire basin to create one direction
and forward speed distribution for a
Divide Atlantic into uniform gridboxes and calculate statistics ineach box
Determine speed and directionstatistics from historical stormswithin a radius of the storm that
Model Year 1, Event 1
Origin location and historical storms
moves w e even
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Tropical Cyclone Event Set Development:
Basin Simulation
Storm Movement
Based on random sampling, direction 10%an spee s e erm ne or o e
Year 1, Storm 1, and its location ismoved ahead 6 hours in time, thenprocess is repeated
45%
Direction and speed distributionsmay be altered based on type of
historical storm track
1%35%
Track calculations usually havememory of previous motion to avoidsharp turns or jumps in motion
1%1%5%
yDensity
Probabilit
Rate of Movement
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Tropical Cyclone Event Set Development:
Basin Simulation
Storm Lysis
At each time step that storm is
Map: Munich Reinsurance America
modeled, there is a probability that
the storm dissipates Probability of Lysis is dependent on
lysis and other physical parameters,such as:
Storm latitude
Over land or water Event 1
Track Model Output
Once track model run for N years is completed (and properly calibrated),
you can discard tropical cyclone tracks that do not impact your locations ofinterest (i.e. storms that stay far out to sea)
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Tropical Cyclone Event Set Development:
Basin Simulation
Track Calibration
Track model is calibrated so that storm counts in each grid box (or area of
region.
At the coast, number of landfalls is usually calibrated by the historicallandfall rate in different coastline segments, or gates.
Gate landfall frequencies are smoothed using data from adjacent gates oroffshore data for regions that often see bypassing storms.
G
Landfall Rate at D = 0.3D + 0.2C +
0.2E + 0.12B + 0.12F +0.04A + 0.04G NC
CD
ESC
suranceAmeric
a
ABGA
Map:M
unichRei
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Tropical Cyclone Event Set Development:
Intensity Calculation (Storm-Scale)
There are several factors that im act a tro icalcyclones intensity and overall wind field
Minimum central pressure
m en sea eve pressures surroun ng e rop ca cyc one
Local frictional effects
Photo: Munich Reinsurance America
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Tropical Cyclone Event Set Development:
Intensity Calculation (Storm-Scale)
Central Pressure Calculation
A minimum central ressure is assi ned to storm at ori in, and isallowed to change with time, based on historical pressure change
distributions in the region.
Little pressure data in much of historical record, however
Pressure will typically decrease (storm becomes more intense) whenstorm is over warm water, regions of typically low wind shear, and is far
from any major land features Pressure will typically increase (storm becomes less intense) when
over cooler waters, in regions of high wind shear, over land, or nearrugged terrain
n mum pressures are usua y cappe ase on s or ca pressuresand physical limits occurring in nature
Based on central pressure and assumed pressure outside the storm,
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Tropical Cyclone Event Set Development:
Intensity Calculation (Storm-Scale)
Initial Wind Field Calculation
There are several different equations or mathematical approximationsthat can be used to simulate a hurricane wind field
Gradient Wind Equation
Holland B Parameter
Etc.
These e uations t icall use central ressure, Rmax, and assumed
pressure outside of storms circulation envelope, along with an assumedwind decay rate (inside and outside the eyewall)
Hurricane winds are calculated on a rid and for each location of interest
for each time step of a stochastic event during landfall
T i l C l E t S t D l t
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Tropical Cyclone Event Set Development:
Example Wind Field (Frictionless)
km/hr
insuranceAmer
ica
Image:
MunichRei
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Tropical Cyclone Event Set Development:
Intensity Calculation (Local-Scale)
Location Wind Intensity
The wind experienced at a given site during a hurricane depends on several
source, pa an s e reg ona c arac er s cs
Source characteristics:
, ,
transition (if occurring)
Path characteristics:
Distance from eyewall, strong or weak side of storm
Site Characteristics:
Upwind locations land use and cover (fetch)
Elevation, topography, or building height
Models typically use peak highest gust at site of interest/grid box over life of
event to estimate damage; some consider both duration and intensity of highwinds
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Tropical Cyclone Event Set Development:
Event Probabilities
Event Set Reduction (optional)
Similar storms in the overall stochastic event set can be removed if thean a ra es are e cons an .
Advantage: Smaller event set, model runs more quickly
Disadvantage: Loss of simulation year data in event set, makesassessing multiple events in a single year difficult.
Event B
Event A
ven a e:
0.00000978
Event B Rate:
Max. Winds:
0.00000978
Discard Event A; Event A rate
Event A: 75 mph
Event B: 78 mph
,becomes:
0.00001956
Map: Munich Reinsurance America
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Hurricane Damage Estimation
Vulnerability Curves
Covers dozens of types of structures and occupancies, as
well as default curves when this information is unknown
, ,
time element / business interruption
Modifiers for different qualities of construction
Sources of Structural Vulnerability Data
Claims data from historical events
Laboratory testing of structures and components
Computer simulations of structural response
Expert analysis and opinion
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Hurricane Damage Estimation
nceAmericaClaims Data Analysis
Amount of dama e re orted in claims for
r rt:MunichReinsur
each construction type or occupancy
compared to modeled wind speed at
location to develop vulnerability curves
ag
eFact
Cha
eanDam
Maximum Wind Gust (mph)
Earthquake
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Earthquake
Modeling Basics
Source: USGS
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Perils included in U.S. Earthquake Models
Explicitly Modeled Perils (Perils included in Event Set/Intensity Calculation):
Ground Shaking
Implicitly Modeled Perils (Perils included via factors and/or vulnerability curves):
Liquefaction
Landslides
Fire Following Earthquake
Earthquake Sprinkler Leakage
Non-Modeled Perils:
Tsunami
Secondary events triggered by earthquake, such as nuclear incidents.
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Peril Models: EarthquakeEarth uake Event Set Develo ment
Identify potential earthquake sources
Assign an appropriate magnitude-frequency relationship and a
corresponding recurrence interval distribution to each source
scre ze e magn u e sca e e ween e owes magn u e
of interest and the maximum magnitude for each source
Distribute events around the source
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Peril Models: EarthquakeEvent Set: Identif Potential Sources
USGS National Seismic Hazard Maps are basis for model EQ sources
Source: California Geological Survey
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Peril Models: EarthquakeEvent Set: Fre uenc / Severit Relationshi s
For each fault, both
historical seismicity
and paleoseismic
studies of sli rates
(where available) are
used to determine the
-
relationship.
Source: California Geological Survey
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Peril Models: EarthquakeEvent Set: Recurrence Interval Distribution
Recurrence Interval Distribution for California (No Subduction Zone EQs)
Magnitude Annual Rate Return Period
5.0 6 2 Months
.
6.0 1 1 Year
6.5 0.8 1.25 Years
7.0 0.1 10 Years
7.5 0.02 50 Years
8.0 0.005 200 Years
For source areas (modeled as pseudofaults), maximum magnitudes will not
e as g as t ose a ong nown au ts.
P il M d l E th k
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Peril Models: EarthquakeEvent Set: Event Rates
For each fault or area source, the frequency-severity relationship is combined
with a probability distribution to get event rates over a given time period (typically
1 year).
Poisson Model
Time Dependent Model
Stress Transfer Model
Only well-researched faults have time-dependent or stress transfer models
associated with them, all other models use Poisson modeling.
P il M d l E th k
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Peril Models: EarthquakeEvent Set: Discretizin
Length of fault determines maximum potential rupture length and magnitude,
and the potential magnitude of a quake along a fault can be any magnitude up
to its maximum.
There is a lot of uncertainty in earthquake magnitudes and the ground shaking
.
same fault or fault segment redundant. For example. the difference in impacts
between a M6.9 versus M6.8 earthquake on same fault segment are within the
hazard modeling uncertainty, so no need to model both magnitudes.
Thus, events are discretized, which means the models have gaps between
, .
This also lowers size of event set.
Usually done in set magnitude increments, fault-dependent
Models only need to consider damaging earthquakes, so a minimum strength
level can also be set in the model
Peril Models: Earthquake
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Peril Models: Earthquake
Event Set: Distributing Events on a Source
Fault X
M7.0
M6.0 (1)
M6.0 (2)
M6.5 (1)
M6.5 (2)
Peril Models: Earthquake
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Peril Models: Earthquake
Event Set: Individual Event Rates
Modeled Event Rates for different magnitude events along a given fault are
Magnitude Rate # Modeled Events Rate Per Event
M5.0 0.1 20 0.005M5.5 0.05 20 0.0025
M6.0 0.01 15 0.0007
. . .
M7.0 0.001 5 0.0002
M7.5 0.0005 2 0.00025
Chart: Munich Reinsurance America
Peril Models: Earthquake
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Peril Models: EarthquakeIntensit Calculation
The spread of the energy released by an earthquake is described by
attenuation equations.
For the United States, a set of attenuation equations are provided bythe U.S. Geological Survey as part of their National Seismic Hazard
,
in their models.
Earthquake Magnitude & Depth
Distance from source
equations, and is dependent on:
Duration of ground motion
Geological conditions along the
wave path
Local Soil Conditions
Peril Models: Earthquake
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Peril Models: EarthquakeIntensit Calculation: Ma nitude
Ma nitude 6.0 Ma nitude 6.9 Ma nitude 7.9
Source: USGS
Peril Models: Earthquake
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Peril Models: EarthquakeIntensit Calculation: De th
Northridge: Magnitude 6.7
Thrust Mechanism, 18 km depth
Nisqually: Magnitude 6.8
Normal Mechanism, 52 km depth
Source: USGS
Peril Models: Earthquake
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Peril Models: EarthquakeIntensit Calculation: Bedrock T e
Source: USGS
Peril Models: Earthquake
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Peril Models: EarthquakeIntensit Calculation: Site Characteristics
Recorded
Time Histories
Recording StationsSan Francisco
Oakland
Distance: 80 km / 50 miles
Yerba Buena Island (Rock)
Treasure Island (Landfill)
Calculated
Response Spectra
San Jose
Epicenter
Map: Munich Re America
Peril Models: Earthquake
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Peril Models: EarthquakeIntensit Calculation
There are two main methods of calculating an earthquakes intensity at a given
location of interest in catastrophe models:
Peak Ground Acceleration A measurement of the maximum pulse of ground
shaking at a location. Describes as a percentage of the acceleration due to
Spectral Acceleration An instrumental calculation combining ground motion,
site response, and building response.
Considers duration, frequency, and type of construction
Vulnerability curves will be calibrated to whatever intensity metric is used.
Earthquake Damage Estimation
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Vulnerability Curves
Covers dozens of types of structures and occupancies, as
well as default curves when this information is unknown
, ,
time element / business interruption
Modifiers for different qualities of construction
Sources of Structural Vulnerability Data
Claims data from historical events
Laboratory testing of structures and components
Computer simulations of structural response
Expert analysis and opinion
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THANK YOU! ANY QUESTIONS?
Mark Bove [email protected]
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Copyright 2013 Munich Reinsurance America, Inc. All rights reserved. "Munich Re" and the Munich Re logo are
internationall rotected re istered trademarks. The material in this resentation is rovided for our information onl , and
is not permitted to be further distributed without the express written permission of Munich Reinsurance America, Inc. or
Munich Re. This material is not intended to be legal, underwriting, financial, or any other type of professional advice.
Examples given are for illustrative purposes only. Each reader should consult an attorney and other appropriate advisors
to determine the applicability of any particular contract language to the reader's specific circumstances.