Casualty Exposure
Rating
CARe Boot Camp 2007
H. Smosna
Reinsurance XOL Pricing
 Per occurrence XOL treaties provide a limit of coverage
in excess of a ceding company’s retention.
 Reinsurance pricing actuaries must calculate expected
loss and ALAE in the layer
 The expected loss & ALAE must be loaded for internal
expense, C&B, profit, contingencies, loss sensitive
features
 This reinsurance ceded premium is usually expressed as
percent of the Ceding Company’s Prospective Subject
Premium
2
What is Exposure Rating?
 Exposure rating estimates expected loss to the
layer for a prospective period
 Exposure rating uses your client’s limits profile,
hazard characteristics, severity curves and gross
loss &ALAE ratio to estimate expected loss to the
layer
 Severity distributions based on industry data are
used to calculate LEVs (Limited Expected Values;
also know as LASs or Limited Average Severities)
 The LEVs are used to estimate losses to the
reinsurance layer by spreading ground up loss into
the desired layer
3
Why Exposure Rate?
 Complement of credibility for experience rate
 Price for ‘free cover’ (when the top of your layer
exceeds the largest trended loss in your data)
 Experience Rate is not credible
 Can adjust experience burns for limits drift
 Can use exposure burns to determine relativity
based burns for higher layers
4
Advantages of Exposure Rating
over Experience Rating
 The current risk profile is modeled
 For a new book of business (so no experience
available) pro forma profiles can be used to
project expected loss to the layer
 The exposure rating exercise is often easy to
perform so UWs can determine an exposure
rating based reinsurance rate as part of their
triage process
5
Exposure Rating – what info do you
need?
 Prospective Ground Up / Gross Loss Ratio for subject






business
Prospective Subject Premium
Limit & Attachment Point Profile with Premium
• Prospective limit and attachment profile
• i.e. 50% of premium is written at a $1 million per
occurrence limit, 25% is written at a $5 million p.o.
limit, 25% is written at a $10 million p.o. limit. All limits
attach excess of a 100K SIR.
Severity distribution/LEVs for the line of business reflecting
hazard level of underlying risks (Table 123ABC, Auto) – see
your UW
Submission data is rarely provided in the full detail
corresponding to the ISO Table definitions
The layer you are pricing
No loss experience to the layer required
6
The Concept
Exposure Factor based on
LEVs = Ceded Loss/Gross
Loss
 Gross Loss Ratio X Exposure Factor =
X
Gross Loss
Gross Premium
= Ceded Loss
Gross Premium
Ceded Loss
Gross Loss
=
Burn, Loss Cost
7
Visualization – limits profile
Policy Limit A
Policy Limit B
Policy Limit C
8
Visualization – Reinsurance layer
Policy Limit A
Top of Reinsurance Layer
Policy Limit B
Bottom of Reinsurance Layer
Policy Limit C
9
Visualization – Ceded Loss
Policy Limit A
Top of Reinsurance Layer
Policy Limit B
Bottom of Reinsurance Layer
Policy Limit C
10
Visualization – Ceded Loss as % of
Gross Loss – Policy A
Policy Limit A
Policy Limit A
Top of Reinsurance Layer
Ceded Loss
Gross Loss
Bottom of Reinsurance Layer
(1) Ceded Loss/Gross Loss =
(2) Gross Loss Ratio =
(1) * (2) = Ceded Loss/Gross Premium =
SP =
Expected Loss to layer =
20.0%
50.0%
10.0%
1,000,000
100,000
11
Visualization – Ceded Loss as % of
Gross Loss – Policy B
Top of Reinsurance Layer
Policy Limit B
Policy Limit B
Ceded Loss
Bottom of Reinsurance Layer
Gross Loss
(1) Ceded Loss/Gross Loss =
(2) Gross Loss Ratio =
(1) * (2) = Ceded Loss/Gross Premium =
SP =
Expected Loss to layer =
8.0%
50.0%
4.0%
1,000,000
40,000
12
Where’s the frequency?
 Again - Severity distributions based on industry data are used to




calculate LEVs (Limited Expected Values; also know as LASs or
Limited Average Severities)
Again - The LEVs are used to estimate losses to the reinsurance
layer by spreading ground up loss into the desired layer
Expected loss = frequency*severity
Exposure Factor based on LEVs = Ceded Loss/Gross Loss
• Ceded loss = [LEV(top) – LEV(bottom)]* frequency
• Gross loss = [LEV(Policy limit) – LEV(0)]* frequency
Frequency cancels out!
13
Limit
 GL policies have 2 kinds of limits:
• Per occurrence
• Annual aggregate
 In this presentation we ignore the effects of
aggregate limits.
• Assume that the primary policy aggregate
limit is high enough and ground up
frequency low enough that agg limit has
minimal effect
 Frequency from previous slide would not cancel
out if considering aggregate limits
14
LEV vs. ILF
 ISO creates severity distributions and from these
they generate ILFs (Increased Limits Factors) –
Tables 1,2,3,A,B,C for example
 ILFs are used to rate primary policies (at 100K
basic limit) to higher limits. They represent the
ratio of all per occurrence costs at policy limit to all
p.o. costs at basic limit
 ILFs include all per occurrence costs at a specific
policy limit:
• Expected limited p.o. loss cost
• All ALAE
• ULAE
• Risk Load
15
LEV vs. ILF – cont’d
 Do not use ISO ILFs in exposure rating
• Risk load and ULAE get in to your calculations
• The expected ALAE per claim for years was assumed to
be the same for all policy limits so was loaded 100% into
the basic limit. So when taking ratios of ILFs the ALAE
would cancel out
• ISO has a new ALAE methodology
 Sometimes the ceding company’s ILFs are the only info
available (ie for an esoteric LOB). May need to use them.
 Use LEVs from the severity distributions
• If you are pricing to a different average DOL than that
underlying the ISO parameters you can adjust the
parameters
• If you don’t like the parameters you can change them too
(make the tail thicker)
16
More on ISO ILFs
 The data underlying ISO ILFS comes from 2 sources:





• individual loss info from primary polices included in the
standard statistical reporting to ISO
• Data from a special ‘call’ for individual loss info from
Umbrella and excess policies
ISO fits a mixture of exponential distributions to empirical
distributions derived from the data
Because the data is sparse in the tail ISO uses a distribution
above some point to smooth the empirical distribution
The mixed exponential (ME) curves are less severe than the
Pareto curves
Curve history: Truncated pareto, Pareto Soup, ME
ISO data falls off at a relatively low level and is very sparse
over 5M
17
Proceed with Caution when using
ISO Mixed Exponential curves
 Not a lot of data above $1M
 M/E fits data closely up to $1M, but excess of
$1 million tail appears to thin
 ME maxes out at 10M
 M/E 4x1 and 5x5 factors are inconsistent, for
example, Premops 2 4x1 factors are lower than
Premops 1
18
Clash – not captured in exposure
rating
 Casualty treaties often cover losses for which
exposure rating does not provide an answer
• A Long-haul trucker collides with an auto
• WC loss from trucker
• CAL loss from individual in the auto
• Treaty will define this as one occurrence
• The WC claim is below the treaty retention
• The CAL claim is below the treaty retention
• Combined the WC &CAL claims pierce the
treaty retention – Clash loss
 Exposure rating also does not estimate for
ECO/XPL
19
What is an LEV?
 Limited Expected Value
• The average size of loss when all losses are limited
to a particular value
• The expected loss from ground up to some limit (k)
k
• LEV(k)=∫xf(x)dx+k[1–F(k)]
0
• x is the severity of an individual claim
• f(x) is the pdf of the severity
• F(x) is the cdf of the severity
20
What is an LEV?
 Limited Expected Value
k
• LEV(k)=∫xf(x)dx+k[1–F(k)]
•
•
•
•
0
For any random variable x, one of two things can happen:
1. x is <= the limitation k
2. x is > the limitation k
The first part of the equation tackles (1) by calculating the
expected loss limited to k when x <= k.
The second part of the equation tackles (2). For any x>k, you
‘cap’ x at k.
The sum of (1) and (2) gives you the average ground up loss
when all losses are limited to k.
21
Empirical LEV Example
Individual Loss Experience
Claim#
1
2
3
4
5
6
7
8
9
10
Ground Up Loss $$$
141,000
16,000
46,000
40,000
351,000
259,000
317,000
1,511,000
107,000
567,000
Limited gu loss at 500k
141,000
16,000
46,000
40,000
351,000
259,000
317,000
500,000
107,000
500,000
Limited gu loss at 1000k
141,000
16,000
46,000
40,000
351,000
259,000
317,000
1,000,000
107,000
567,000
0
0
0
0
0
0
0
500,000
0
67,000
Loss in 500K to 1000K layer
LEV@500K =
(141,000+16,000+46,000+40,000+351,000+259,000+317,000+500,000+107,000+500,000)/10 =
227,700
LEV@1000K =
(141,000+16,000+46,000+40,000+351,000+259,000+317,000+1,000,000+107,000+567,000)/10 =
284,400
LEV@1000K - LEV@500K
Just take the difference of 284,400 and 227,700
56,700
LEV@1000K - LEV@500K
(0+0+0+0+0+0+0+500,000+0+67,000)/10 =
56,700
If you want to know what percent of loss is in the 500x500K layer on a 1M policy take the
ratio:
LEV@1000K - LEV@500K
LEV@1000K
22
=
56,700
284,400
=
20%
The Concept - again
Exposure Factor based on
LEVs = Ceded Loss/Gross Loss
 Gross Loss Ratio X Exposure Factor =
Gross Loss
Gross Premium
X
Ceded Loss
Gross Loss
= Ceded Loss
= Burn, Loss Cost
Gross Premium
 Credibility weight exposure burn with experience burn and then load up Z

weighted burn for expenses, profit, etc to derive reinsurance rate
Reinsurance rate * Subject Premium = Ceded Premium
23
Exposure Rating – what info do you
need?
 Ground Up Loss Ratio for the subject business
55%
24
Exposure Rating – what info do you
need?
 The Layer you are pricing:
Reinsurance Limit
Reinsurance Retention:
Effective Limit:
Effective Retention:
1st Layer
750,000
1,250,000
750,000
1,250,000
If ALAE is included in the limit the effective
reinsurance limit and retention should be
reduced by the ALAE load
25
ALAE
 ALAE in reinsurance contracts:
• Pro-rata
• Included with loss
 ALAE in primary policies
• Unlimited (ISO) or outside the limit
• Included in limit
26
ALAE
 Assume the primary policy’s ALAE is unlimited (as
per ISO)
 When reinsurance treatment of ALAE is prorata:
• Estimate ratio of ALAE to loss and load in (use
a gross loss & alae ratio when deriving your
burn)
 When ALAE is included with loss
• Correct way is complicated
• Can reduce attachment point and limit by
dividing both by (1 + XOL ALAE%)
27
Exposure Rating – what info do you
need?
 Limits Profile
SIR
100,000
250,000
300,000
750,000
1,000,000
100,000
250,000
300,000
500,000
1,000,000
Limit
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
2,000,000
2,000,000
2,000,000
2,000,000
2,000,000
28
Premium
0.2%
6.2%
5.1%
72.5%
6.5%
0.0%
0.7%
0.6%
7.8%
0.7%
Exposure Rating – what info do you need? ….Severity
distribution/LEVs for the line of business reflecting hazard level of
underlying risks
5 Parameter Pareto
2002 Premops 1 - Multistate
2002 Premops 2 - Multistate
2002 Premops 3 - Multistate
2002 Premops 1 - CA
2002 Premops 2 - CA
2002 Premops 3 - CA
2002 Premops 1 - FL
2002 Premops 2 - FL
2002 Premops 3 - FL
2002 Premops 1 - IL
2002 Premops 2 - IL
2002 Premops 3 - IL
2002 Premops 1 - NJ
2002 Premops 2 - NJ
2002 Premops 3 - NJ
2002 Premops 1 - NY
2002 Premops 2 - NY
2002 Premops 3 - NY
2002 Premops 1 - OH
2002 Premops 2 - OH
2002 Premops 3 - OH
2002 Premops 1 - PA
2002 Premops 2 - PA
2002 Premops 3 - PA
2002 Premops 1 - TX
2002 Premops 2 - TX
2002 Premops 3 - TX
2002 Products A
2002 Products B
2002 Products C
2002 CCA Lt Grp 1
2002 CCA Hvy Grp 1
2002 CCA XHvy Grp 1
29
Mixed Exponential
2003 ISO CCA Liab Lt - Grp 1
2003 ISO CCA Liab Hvy - Grp 1
2003 ISO CCA Liab XHvy - Grp 1
2003 ISO CCA Liab All Other - Grp 1
2003 ISO CCA Liab Lt - Grp 2
2003 ISO CCA Liab Hvy - Grp 2
2003 ISO CCA Liab XHvy - Grp 2
2003 ISO CCA Liab All Other - Grp 2
2003 ISO CCA Liab Lt - Grp 3
2003 ISO CCA Liab Hvy - Grp 3
2003 ISO CCA Liab XHvy - Grp 3
2003 ISO CCA Liab All Other - Grp 3
2003 ISO CCA Liab Lt - Grp 4
2003 ISO CCA Liab Hvy - Grp 4
2003 ISO CCA Liab XHvy - Grp 4
2003 ISO CCA Liab All Other - Grp 4
2003 ISO CCA Liab Lt - Grp 5
2003 ISO CCA Liab Hvy - Grp 5
2003 ISO CCA Liab XHvy - Grp 5
2003 ISO CCA Liab All Other - Grp 5
2003 ISO CCA Liab Lt - Grp 6
2003 ISO CCA Liab Hvy - Grp 6
2003 ISO CCA Liab XHvy - Grp 6
2003 ISO CCA Liab All Other - Grp 6
2003 ISO CCA Liab Zone Rated
2006 ISO Premops 1 - Multistate
2006 ISO Premops 2 - Multistate
2006 ISO Premops 3 - Multistate
2006 ISO Premops 1 - Group A
2006 ISO Premops 2 - Group A
2006 ISO Premops 3 - Group A
2006 ISO Premops 1 - Group B
2006 ISO Premops 2 - Group B
2006 ISO Premops 3 - Group B
Severity Distributions : Mixed
Exponential LEVs
 Send ISO a check
•
For the mixed exponential you will receive
the parameters, weights and closed form
formula - all you need to build your own
exposure model
• ME closed form formula:
LEV = ∑ wjλj [1 – e –(x/λ)]
8
J=1
Selected ILF Table
2006 ISO Premops 2 - Group B
Selected ILF Table
2006 ISO Premops 2 - Group B
Weight
100
Weight
100
1
2
1,366
1
0.4927620
6,823
2
0.3169920
3
31,157
Mixed Exponential Parameters
4
5
6
98,452
500,542
2,074,148
7
9,146,627
ISO Weight Given to Mixed Exponential Parameters
3
4
5
6
0.1130270
0.0565070
0.0182380
0.0020360
30
7
0.0004380
8
1
8
-
Severity Distributions : 5 Parameter
Pareto LEVs
 For the 5 Parameter Pareto you need the
parameters and closed form formula – and you
can build your own exposure model
• 5PP closed form formula:
LEV = P*S + [(1-P)/(Q-1)] * [(B+Q*T)(B+x)*{(B+T)/(B+x)}^Q] for Q>1
Selected ILF Table
2002 Products A
Weight
100
B
5 Parameter Pareto Parameters
P
S
Q
57,584
1.39
31
0.97
5,131
T
XOL ALAE%
58,557
23.00%
Appropriate LEVs – not that simple.
 Rare to receive data from the ceding company that maps


perfectly to ISO severity distributions
In the example below we are deriving LEVs for an
Umbrella profile
• Umbrella policies are exposed by underlying GL, AL,
EL policies
• In exposure rating umbrella we want our LEVs based
on a weighting of the underlying , varied exposures
Your exposure rating model should have the capability of
deriving LEVs based on weighting together the exposure
factors from the various severity distributions
Selected ILF Table
2002 Premops 1 - Multistate
2002 Premops 2 - Multistate
2002 CCA Hvy - Grp 2 (Big Grp)
2002 CCA XH - Grp 2 (Big Grp)
2002 Products B
2002 Products C
Weight
15
15
20
20
15
15
B
5 Parameter Pareto Parameters
P
S
Q
T
XOL ALAE%
15,020
1.38
0.97
4,813
58,557
14.00%
186,831
1.68
0.96
7,058
58,557
14.00%
378,277
1.56
0.98
6,814
18,178
6.00%
431,825
1.55
0.98
7,688
18,178
6.00%
271,585
1.65
0.93
10,474
58,557
23.00%
313,990
1.64
0.88
13,479
58,557
23.00%
32
An Example: Select a Limit band
from the sample profile
 Underlying Policy = 500,000
 Policy Limit = 2,000,000
 This represents 7.8% of the premium
 Reinsurance Attachment Point = 750,000
 Reinsurance Limit = 1,500,000
You will use LEVs from a severity distribution to allocate
ground up expected loss to layers
 LEV @ 500,000 = 10,518
 LEV @ 2,000,000 + 500,000 = 12,630
 LEV @ 750,000 = 11,149
 LEV @ 1,500,000 + 750,000 = 12,527
33
How does the reinsurance apply?
STOP: Read your contract!
 Who wrote the underlying policy?
• Is the Umbrella supported (over the ceding
company’s own primary)?
• Is the Umbrella unsupported (over another
company’s primary policy)?
 How does the reinsurance respond?
• If supported (over their own) typically the
reinsurance attaches from the ground up
• If unsupported (over other’s primary) the
reinsurance attaches on top of the
underlying
 How is Subject Premium defined?
34
First some simple examples:
Umbrella Policy
Umbrella
11M
10M
Umbrella
1M
Underlying
Reinsurance: 4x1M
35
First some simple examples: Umbrella
policy with a 4M ground up loss
Umbrella
11M
4M
1M
Reinsurance: 4x1M
Ground Up Loss: 4M
36
First some simple examples:
Reinsurance payment when over own
Umbrella
11M
4M
3M
2M
1M
Reinsurance: 4x1M from gu
Ground Up Loss: 4M
Reins payment/over other: 3M (excess of 1M)
37
First some simple examples:
Reinsurance payment when over other
underlying
Umbrella
11M
4M
3M
2M
1M
Reinsurance: 4x1Mx1M UL
Ground Up Loss: 4M
Reins payment/over other: 2M (excess of 2M)
38
A bit trickier: The Policy
2M policy limit xs 500K UL
250K
250K
250K
250K
2M
250K
250K
250K
250K
250K
500K
250K
39
A bit trickier: The Reinsurance
Layer
1.5M reins limit xs 750K client retention
250K
250K
250K
1.5M
250K
250K
250K
250K
750K
250K
250K
40
The Policy & the Reinsurance Layer –
OVER THEIR OWN/reinsurance
attaches from the ground up
2.50M
250K
2.25M
250K
250K
250K
1.5M
250K
250K
250K
750K
250K
500K
250K
250K
UL = underlying policy limit or SIR (500,000)
PL = Policy Limit (2,000,000)
AP = Attachment Point of Reinsurance (750,000)
Lim = Limit of Reinsurance (1,500,000)
41
Exposure Factor/OVER THEIR OWN
 Your exposure factor = ceded loss/gross loss
 Your ceded loss is the expected ground up loss at 2.25M less the expected ground
up loss at 750K
 Your gross loss is the expected ground up loss at 2.5M less the expected loss at
the 500K underlying
 Using LEVs the exposure factor =
• [LEV(2.25M) – LEV (0.75M)]/[LEV(2.5M) – LEV(0.5M)]
2.50M
250K
2.25M
250K
250K
250K
1.5M
250K
250K
250K
750K
250K
500K
250K
250K
42
The Policy & the Reinsurance Layer –
OVER OTHER’S/reinsurance attaches
on top of the underlying
2.50M
250K
250K
1.5M
250K
250K
2.0M
250K
1.25M
250K
750K
250K
250K
500K
250K
250K
UL = underlying policy limit or SIR (500,000)
PL = Policy Limit (2,000,000)
AP = Attachment Point of Reinsurance (750,000)
Lim = Limit of Reinsurance (1,500,000)
43
Exposure Factor/OVER OTHER’S
 Your exposure factor = ceded loss/gross loss
 Your ceded loss is the expected ground up loss at 2.5M less the expected ground
up loss at 1.25M
 Your gross loss is the expected ground up loss at 2.5M less the expected loss at
the 500K underlying
 Using LEVs the exposure factor =
• [LEV(2.5M) – LEV (1.25M)]/[LEV(2.5M) – LEV(0.5M)]
2.50M
250K
250K
1.5M
250K
250K
2.0M
250K
1.25M
250K
750K
250K
250K
500K
250K
250K
UL = underlying policy limit or SIR (500,000)
PL = Policy Limit (2,000,000)
AP = Attachment Point of Reinsurance (750,000)
Lim = Limit of Reinsurance (1,500,000)
44
Pull it all together
In the “over their own” scenario; the exposure
factor
= [LEV(2.25M) – LEV(0.75M)]/[LEV(2.5M) –
LEV(0.5M)]
= (12,527 – 11,149)/(12,630 – 10,518)
= 65%




LEV @ 500,000 = 10,518
LEV @ 2,000,000 + 500,000 = 12,630
LEV @ 750,000 = 11,149
LEV @ 1,500,000 + 750,000 = 12,527
45
Pull it all together
SIR
100,000
250,000
300,000
750,000
1,000,000
100,000
250,000
300,000
500,000
1,000,000
Total:
Limit
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
2,000,000
2,000,000
2,000,000
2,000,000
2,000,000
Premium
0.2%
6.2%
5.1%
72.5%
6.5%
0.0%
0.7%
0.6%
7.8%
0.7%
100%
1st Layer
Ceded Loss
as a % of
Gross Loss
15.08%
28.75%
34.15%
100.00%
100.00%
29.96%
43.92%
48.10%
65.24%
78.25%
88.54%
For this 1.5 x 0.75M layer the weighted
exposure factor is 88%
46
Pull it all together
 Gross Loss Ratio X Exposure Factor =
Gross Loss
Gross Premium
X
Ceded Loss
Gross Loss
= Ceded Loss
= Burn
Gross Premium
= 55% X 88% = 49%
IF Subject Premium = 10M the expected loss to
the 1.5 x 0.75M layer is $490,000
Gross up for expense, profit, et al and you have
your reinsurance ceded premium
47
Data Issues
 Limits profile
• Broad ranges
• Limits profile separate from attachment point
profile
• Count based (to fix, multiply by the LEV at
corresponding policy limit)
• Premium from profile doesn’t reconcile well
with historical or projected premium
• Do you have all business units,
companies?
• PPA split limits (10/20 per person/per occ)
 ILF table breakdown
48
Free Cover
 In your experience rating no losses have trended
into the highest portion of the layer you are pricing
 Example:
• You are pricing a 750x250K layer
• Largest trended loss is 500K from ground up
• Your experience burn will be the same for your
750x250K layer as for a 250x250K layer
Trended Ground Up
Claims
500,000
400,000
300,000
200,000
100,000
Loss to 250x250K layer
250,000
150,000
50,000
-
49
Loss to 750x250K layer
250,000
150,000
50,000
-
Free Cover – cont’d
 One solution:
• Split the layer you are pricing (750x250K) into 2 pieces:
• 250x250K
• 500x500K
• If deemed credible, use the experience burn as your selected
burn for the lower part of your layer OR credibility weight your
experience and exposure burns to derive your selected burn
• Then use exposure burn relativities to derive the burn for the
upper part of your layer
• Sum the selected burns for the two parts of the layer you are
pricing to derive the full layer selected burn
Layer
250x250K
500x500K
Experience Burn
750x250K
Exposure Burn
10.0%
0.0%
Selected Burn
12.0%
11.0%
6.0%
5.5%
10.0%
18.0%
Where 5.5% = 11% * (6%/12%)
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16.5%
Problems with experience rating
 Presence or absence of a few large claims drives the






indicated rates.
If the book of business has been shifting
Can be difficult to estimate LDFs, trend, OLFs
There may be significant data issues
Trending individual claims past policy limits.
Impact of current policy limit profile vs. historical
profile.
History not reflective of current situation: reserving
practices, type of business, coverage, etc.
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Problems with experience rating –
Limits Drift
 Your limits profile is shifting/drifting upwards
• In 2006; 8% of your policies were at limits
of 2M
• Now , 13% of your policies are at 2M
• You can use an exposure approach to
adjust your AY experience burns for limits
drift
 Problem: need historical limits profiles
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Problems with experience rating –
Limits Drift
profile
2006
2007
prem weight
ILF
Expected Loss 1x1 weighted el 1x1
100,000
2.0%
500,000
30.0%
1.10
1,000,000
60.0%
1.25
0.0%
2,000,000
8.0%
1.70
26.5%
100,000
2.0%
500,000
20.0%
1.10
0.0%
1,000,000
65.0%
1.25
0.0%
2,000,000
13.0%
1.70
26.5%
limits drift factor
0.0%
0.0%
2.12%
1.625
3.44%
1.000
0.0%
26.5% = 1-(ILF@1M/ILF@2M) or the ceded loss/gross loss
1.625 = .0344/.0212
Adjust your experience burn from AY 2006 by a factor of
1.625 to correct for the fact that the cedant is writing a
higher percentage of 2M policies than in the past
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How credible is my exposure rating
result?
 Is my exposure curve a good fit ?
 Do I have enough information in the
submission to determine the hazard profile
(Tables 1,2,3,A,B,C, Auto Tables)
 Is my limit&attachment point profile a good
representation of the prospective treaty year
exposure?
 What is the basis for my gross loss ratio?
 Is there anything I am not modeling (i.e.
clash)?
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Unique Application of Exposure Rating
- Umbrella Pricing Adequacy
See CARe 2006
presentation for more
on this topic
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Caveat
 Any pricing tool is only a first step towards
determining adequate reinsurance premium
 Note when modeling or data assumptions are
not met then try to adjust, correct, supplement.
 If you can’t adjust, correct or supplement then
ignore or discount your result!
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The End 
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