Have a (Re)/Insurance contract you think can't be modeled in RMS's Contract Definition Language, CDL? Challenge RMS to model any re/insurance contract in RMS's Contract Definition Language by hashtagging #StumpStumpo on twitter. http://ow.ly/wgP0B

1. ©2014 Risk Management Solutions, Inc. 1
#StumpStumpo – CDL Challenge
Five Minutes into Exceedance 2014, RMS’s CEO Hemant Shah issued the Stump Stumpo
challenge. Tweet a re/insurance contract with hashtag #StumpStumpo and Cody Stumpo, the
Structure Language & CDL product manager, will see if it can be expressed in RMS’s Contract
Definition Language. CDL has the benefit of making simple things simple, and complex things
possible. In these cases, we are definitely focusing on the back half of that sentence. Here are
the results, from both twitter and in-person challenges at Exceedance. If you want to try your
hand at #StumpStumpo, tweet with that hashtag or just email cody.stumpo@rms.com.
1) Increasingly common in California Earthquake market, a Difference in Conditions policy
where the entire account schedule erodes the attachment but only select locations are
covered.
The solution uses the idea of covers taking other covers as their subject. A tree of covers can
be formed in this way, and the contract pays the sum of top-level covers (those not the subject
of some other cover).
 Make a sub schedule of everything but the covered locations (call it OtherLocs), and put
a 10M limit on that
 Make a sub schedule of the covered locations (call it DIC) and pass that through
unlimited
 Put the 10 xs 10 layer on top of the sum of those two.
Covers
C1: 100% Share of 10M to OtherLocs
C2: 100% Share to DIC
C3: 100% Share of 10M xs 10M on C1, C2
Let’s run some losses through to see it’s working how we expect. The contract has one top-
level cover, C3, so C3 is also the contract payout.
Subject Loss 10M to otherlocs to DIC
10 x 10 on C1,
C2
OtherLocs DIC C1 C2 C3
0 5 0 5 0
0 10 0 10 0
0 15 0 15 5
0 20 0 20 10
5 0 5 0 0

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5 5 5 5 0
5 10 5 10 5
5 15 5 15 10
5 20 5 20 10
10 0 10 0 0
10 5 10 5 5
10 10 10 10 10
10 15 10 15 10
10 20 10 20 10
15 0 10 0 0
15 5 10 5 5
15 10 10 10 10
15 15 10 15 10
15 20 10 20 10
2) One actually came in via twitter and could be answered in twitter’s 140-character limit
as well.
This solution uses the capability of a cover to have a payout function (in this case a constant)
other than the usual limit.

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The “Slope” cover pays the 1st 1M of loss. The “FlatLine” cover pays a flat negative 1M upon
its 1M attachment being met. Those two covers work together to create the reverse franchise
(pay the first 1M, but pay 0 for losses above 1M). The “Agg” cover is on the other two covers,
meaning it takes their input as its subject. It then applies the 10M aggregate limit.
+ =
On each graph above, the horizontal axis is the Subject and the vertical axis is the Payout.
3) Another verbally delivered challenge – the assumed ceded swap. Two reinsurers want
to effectively swap treaties. The standalone risk of the two treaties is similar even
though they are exposed to different region / perils. Because of how the treaties
correlate to the reinsurer’s portfolios, they each find the other’s treaty more attractive.
To model this, the challenge is not so much about CDL but the larger concept of Structure
Language. While CDL is the heart of Structure Language, Position statements are the other
small piece, but one that does a lot.
The subject of each contract is a position, and the payout of each contract is a position. These
payouts can be manipulated via simple operations (e.g. plus, minus, scale,…) to form other
positions – which themselves can be the subject of other contracts or of reports. With this
simple ability, it is easy to quickly create structures that model the cash flows and accounting
needs of the industry.
Structure Builder is an application that can depict a Structure graphically – it generates this
picture based on the text of the Structure. The Blue positions are for Reinsurer1 and the
Orange positions are for Reinsurer2. It should be noted that the arrows in the current version
of Structure Builder depict dependency, not loss flow.

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Structure
RI1:Assumed is RI1:Cat1 + RI1:FromRI2
RI2:Assumed is RI2:Cat2 + RI2:FromRI1
RI1:Ceded is RI2:FromRI1
RI2:Ceded is RI1:FromRI2
RI1:Net is RI1:Assumed - RI1:Ceded
RI2:Net is RI2:Assumed - RI2:Ceded
Contract
Declarations
Name is RI1:Cat1
Subject is Cedant1
Description is {RI1's Treaty}
Covers
100% Share of 25M xs 10M
Contract
Declarations
Name is RI2:Cat2
Subject is Cedant2
Description is {RI2's Treaty}
Covers
100% Share of 25M xs 20M
Contract
Declarations
Name is RI2:FromRI1
Subject is RI1:Cat1
Description is {RI1 -> RI2}
Covers
100% Share
Contract
Declarations
Name is RI1:FromRI2
Subject is RI2:Cat2
Description is {RI2 -> RI1}
Covers
100% Share

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4) An emailed challenge – a contract with different layers by peril, an overall aggregate
limit, and a drop-down for the EQ layer.
Well, this almost stumped me. Most of it follows straight off from the description, but the major
question is how to get the drop to pay only under the proper circumstances, and how to get it
to see the full subject in order to apply its layer.
WSCover: 100% Share xs 240 by WS
EQTop: 100% Share of 100 aggregate xs 270 by EQ
EQDrop: 100% Share of 100 aggregate xs 220 on ??
EQOcc: 100% Share of 100 on EQTop, EQDrop
Agg: 100% Share of 200 aggregate on Occ
The EQOcc cover ensures that we do not double pay any losses between EQTop & EQDrop.
The Agg cover puts an annual aggregate limit on losses from Wind, EQTop, & EQDrop.
We want the subject of Drop to be all EQ losses after EQtop exhausts. Putting a cover on
EQTop xs 100 Aggregate Franchise, and putting EQDrop on that, ensures that EQDrop will
only see losses exactly when EQTop is exhausted. But we don’t want EQDrop at that point to
see losses that have already been reduced by the xs 270 of EQTop. So we’ll make the payout
of this intermediate cover be exactly what is not paid by EQTop.
Covers
WSCover: 100% Share of 100 xs 240 by WS
EQTop: 100% Share of 100 Aggregate xs 270 by EQ
Slider: 100% Share of Pay (SubjectOf(EQTop) – EQTop) xs 100 Aggregate on EQTop
EQDrop: 100% Share of 100 xs 220 on Slider
EQOcc: 100% Share of 100 on EQTop, EQDrop
Agg: 100% Share of 200 Aggregate on WSCover, EQOcc
How does this work? The EQTop has a 100 Aggregate Limit, so stops paying after that.
EQDrop is on Slider, which will make it see the full EQ loss minus the EQTop payout - but
because it is xs the same 100 Aggregate that is the limit of EQTop, only once the EQTop Limit
is exhausted.
The EQOcc cover ensures that even in a very large event the EQ payout is only 100.
A Contract’s payout is the sum of the payouts of its top level covers (those covers that are not
the subject of some other cover). In this case, there is just one top level cover, Agg. So in the
examples below, consider the payout of the Agg cover to be the payout of the contract.

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Example 1) An Earthquake sequence arrives: 800, 300.
800 300
Subject Payout Subject Payout
WSCover 0 0 0 0
EQTop 800 100 300 0
Slider 100 700 0 300
EQDrop 700 100 300 80
EQOcc 200 100 80 80
Agg 100 100 80 80
Example 2) An earthquake sequence arrives 300, 800
300 800
Subject Payout Subject Payout
WSCover 0 0 0 0
EQTop 300 30 800 70
Slider 30 0 70 730
EQDrop 0 0 730 100
EQOcc 30 30 170 100
Agg 30 30 100 100

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Example 3) An earthquake sequence arrives 340, 300
340 300
Subject Payout Subject Payout
WSCover 0 0 0 0
EQTop 340 70 300 30
Slider 70 0 30 270
EQDrop 0 0 270 50
EQOcc 70 70 80 80
Agg 70 70 80 80
5) Double place a layer with no protection underneath – this still legally counts as
reinsurance since you cannot recover more than you lose.
The share of a cover is not limited to the 0-100% range, as there are many anticipated use
cases where you might want something else.
Covers
200% Share of 50M xs 50M
Indeed we can see that Payout < Subject for all possible claims of Subject and so it is
reinsurance and not speculation.
6) Another verbally delivered challenge – a per risk with the smaller of a certain constant
amount and each location’s Fire PML as the per risk limit. The per risk contracts are on
an annual basis but have an interlocking clause.
An inelegant solution certainly exists – determine outside the product for each location what
the effective risk limit is and make a cover in the treaty with that limit to the location. (Perhaps
gather all those that have the same limits into per risk covers)

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Contract
Declarations
…
Risk is Each Location
Covers
Pr225: 30% Share of 225M to HighValue per risk
Pr150: 30% Share of 150M to Schedule150 per risk
PR155: 30% Share of 155M to Schedule155 per risk
… //many more covers potentially
occ: 100% Share of 270M on PR225, PR150, PR155,…
We can take advantage of the extensible data model to provide a more elegant solution. Any
tenant will be able to add a field to the Location object. In this case add a field to your risk
locations called e.g. FirePML and populate it at each Location with the Monetary Value of the
Fire PML for that Location. CDL could then see that value and consume it in formulas. This
makes the essence of the per risk contract a one-liner.
pr: 30% Share of min (225M, FirePML) per risk
It’s not quite that magical. FirePML in that line is actually a user-defined CDL function that
reads the FirePML field from the location. Similar to the RMS-defined function RCV that reads
the RCV of the location. (e.g. a deductible that is ‘2% RCV Covered to Location6 by EQ).
Users can extend CDL via their own functions to do all kinds of interesting jobs like this. A
contract then contains a declaration to point to a domain data scheme e.g.
Using StevesExtensions {15 Apr 2014}
Now that contract can use any of the referenced data and functions AND it will provide the
same result on any tenancy that has been provided StevesExtensions {15 Apr 2014}
As per challenge #3 above, we will use Structure Language to properly model the interlocking
clause. An interlocking clause across per risk treaties can be modeled as a contract whose
subject is the treaties, and who applies a layer to that subject. The key is that position
management allows this contract to take other treaties as its subject, and further - not have the
intermediate contracts contribute to overall ceded or net.

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Structure
Construction_2014 is
{Construction Book} / {Inception in 2014}
Construction_2013 is
{Construction Book} / {Inception in 2013}
PerRisk is PR2013 + PR2014
Net is {Construction Book} - Interlocking
Contract
Declarations
Name is PR2013
Subject is Construction_2013
Inception is 1 Jan 2013
Expiration is 31 Jan 2013
Attachment Basis is Risk Attaching
Covers
pr: 30% Share of min (225M, FirePML) per risk
occ: 100% Share of 270M on pr
Contract
Declarations
Name is PR2014
Subject is Construction_2014
Inception is 1 Jan 2014
Expiration is 31 Jan 2014
Attachment Basis is Risk Attaching
Covers
pr: 30% Share of min (225M, FirePML) per risk
occ: 100% Share of 270M on pr
Contract
Declarations
Name is Interlocking
Subject is PerRisk
Covers
100% Share of 270M

10. ©2014 Risk Management Solutions, Inc. 10
7) Another Structure Builder case. A cat treaty generates both payout (from reinsurer to
cedant) and reinstatement premium (from cedant to reinsurer). Cedant would like to
see their net position net of reinstatement premium. Meanwhile, the reinsurer buys retro
on the cat treaty payout only. They too would like to see their net net position.
For transparency’s sake in the diagram, I’ve simply modeled the reinstatement premium in it’s
own contract.
Structure
NetOfRIP is
CatTTY - CatTTY.RIP
Cedant:Net is
Cedant:UNL - NetOfRIP
Reinsurer:Net is
NetOfRIP - Outward:Retro
Contract
Declarations
Name is CatTTY
Subject is Cedant:UNL
Description is {Payout}
Covers
100% Share of 10 xs 10
Contract
Declarations
Name is CatTTY.RIP
Subject is Cedant:UNL
Description is {ReinstPremium}
Covers
10% Share of 10 xs 10 Aggregate
Contract
Declarations
Name is Outward:Retro
Subject is CatTTY
Description is {Retro}
Covers
100% Share of 3 xs 3

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8) An anonymous challenge – each location has a deductible but the policy deductible in
an event is just the largest deductible taken.
CDL anticipates exactly this case with its control over the interaction type of deductibles. Each
deductible can have its own scope. In settling a claim, deductibles interact with deductibles of
smaller scope and that interaction is controlled via the interaction function. The three
interaction functions available currently are min, max, and single largest. Future developments
will allow other interaction types such as controlling exactly which smaller-scoped deductibles
contribute to the larger-scoped deductible (e.g. non-ranking deductibles, in-sequence
deductibles). In the case of location deductibles vs. a policy deductible, the policy deductible
has larger scope than any location deductible and so takes their output as part of its input.
For all the examples, let’s imagine:
Location Deductible Loss
1 100 500
2 200 150
3 300 0
So there are 250 of deductibles taken from the locations.
Min(100, 500) + Min (200, 150) + Min (300, 0) = 250
A standard policy deductible of 300 would first apply to the Subject loss of (500 + 150) and say
Min (300, 650) = 300.
If the policy deductible is of interaction type min, it compares 300 to 250 and takes the larger
(the deductible has to be at a minimum 300) as the effective deductible in this event.
Deductibles
100 to Location1
200 to Location2
300 to Location3
300
Notice the policy deductible does not have any subject constraint – it’s scope is the contract
subject.
If the policy deductible is of interaction type max, it compares 300 to 250 and takes the smaller
(the deductible can be at maximum 250) as the effective deductible in this event.
Deductibles
100 to Location1
200 to Location2
300 to Location3
300 Max

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A Single Largest Deductible doesn’t have an amount. Nor for that matter does it have the
ability to be standard or franchise or any other functional form. It simply selects the single
largest deductible actually taken from amongst deductibles of smaller scope and uses that one
going forward while refunding the rest. The effective deductible in this event would be 150.
Deductibles
100 to Location1
200 to Location2
300 to Location3
Single Largest