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2. Agenda. Typical PuzzleImprovements to Traditional MethodsAnalogy to ReservingHybrid: Experience / Exposure MethodOverriding AssumptionsTesting Default ParametersUS and Global Benchmarks. 3. Reinsurance Proposal. Layer $100,000 xs $100,000Estimated Premium: $40,000,000 GL BusinessSouthe
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1. 1 Solving the Puzzle: The Hybrid Reinsurance Pricing MethodJohn Buchanan - Platinum ReinsuranceCARe � LondonCasualty Pricing Approaches16 July, 2007
2. 2 Agenda Typical Puzzle
Improvements to Traditional Methods
Analogy to Reserving
Hybrid: Experience / Exposure Method
Overriding Assumptions
Testing Default Parameters
US and Global Benchmarks
3. 3 Reinsurance Proposal Layer $100,000 xs $100,000
Estimated Premium: $40,000,000
GL Business
Southeast US
Underwriting and Claims Info
4. 4 Traditional Methods
5. 5 What�s your final answer? Experience for this layer is half of the Exposure
Exposure = 3.92% (1.57 mm)
Experience = 1.85% (0.74 mm)
Trick Question�
6. 6 Traditional Na�ve Approach Na�ve approach
Estimate Exposure Rate � X
Estimate Experience Rate � Y
Combine as w(X)+(1-w)Y
It may be tempting to think the next step is to refine the estimate of w
Not easy, but luckily, not the right next step
7. 7 Better Approach Use the Experience results of the layer, and adjacent layers to examine the Exposure rating assumptions
Use the Exposure rating assumptions to help distinguish noise from signal in the Experience rating
Use claim count to emphasize signal over noise � Exposure model can help provide expected frequencies
8. 8 Better Approach continued Apply forensic actuarial techniques to bring the Exposure and Experience models closer together
Apply the Hybrid method to the adjusted Exposure and Experience models to arrive at the Hybrid answer
Optionally, weight the answer with the Exposure indication. Ideally, the indications are now much closer, so the exact value of the weight is less important.
9. 9 Better Approach Reserving Analogy
10. 10 Exposure Pricing(before investigation)
11. 11 Experience Pricing(before investigation)
12. 12 Exposure and Experience Comparison
13. 13 Overall Pricing Process We don't really know what exposure curve applies to a given account (e.g. we don't know that LN = 50k and CV = 400% is the true underlying distribution)
We have a hunch based on established curves (e.g. we postulate LN = 50k and CV = 300%)
We obtain some observations from a certain number of claims over a certain number of years
in the long run the results will track with the true underlying distribution in 1 but these observations will initially be compared to the hypothesis given in 2
If we make enough correct adjustments to the observations and underlying exposures then we will start to see a non-constant pattern in the ratios of the observed experience results to the initially selected exposure results (the Hybrid ratios).
In this example, the actual Experience will end up being heavier for the top layers
If credible, this lack of constant Hybrid ratios creates a pressure to fatten the tail of the exposure distribution. Making this change to the exposure curve will allow us to create a better balance (e.g. Hybrid ratios will all be closer to 100%).
14. 14 Overriding Assumptions of the Hybrid Method In theory, with perfect modeling and sufficient data the results under the Experience and Exposure methods will be identical.
In practice,
if the model and parameter selections for both Experience and Exposure methods are proper and relevant,
then the results from these methods will be similar,
except for credibility and random variations.
Lower layer experience helps predict higher less credible layers.
Frequency is a more stable indicator than total burn estimates.
15. 15 Basic Steps of The Hybrid Method Step 1: Estimate Experience burns & counts
Step 2: Estimate Exposure burns & counts
Step 3: Calculate Experience/Exposure frequency ratio by attachment point
Step 4: Review Hybrid frequency ratio patterns
Adjust experience or exposure models if needed and re-estimate burns (!!)
Step 5: Similarly review excess severities and/or excess burns
Step 6: Combine Hybrid frequency/severity results
Step 7: Determine overall weight to give Hybrid
16. 16 Step 4-Review Hybrid Frequency Ratios
17. 17 Steps 1-7: Bringing it All Together
18. 18 Example #2 (adjusting Experience for historically higher policy limits)
19. 19 Example #3 (adjusting Exposure for clash potential)
20. 20 Benefits of Hybrid Method One of main benefits is questioning Experience and Exposure Selections
To the extent credible results don�t line up, this provides pressure to the various default parameters
For example, there would be downward pressure on default exposure ILF curves or loss ratios if
Exposure consistently higher than experience, and
Credible experience and experience rating factors
A well constructed Hybrid method can sometimes be given 100% weight if credible
Can review account by account, and aggregate across accounts to evaluate pressure on industry defaults
21. 21 Test of Default Parameters Aggregate across �similar� accounts to evaluate pressure on industry defaults
May want to re-rate accounts using e.g. default rate changes, ILFs, premium allocations, LDFs, trends, etc.
Each individual observation represents a cedant/attachment point exper/expos ratio
Review dispersion of results and overall trend
E.g. if weighted and/or fitted exper/expos ratios are well below 100% (or e.g. 90% if give some underwriter credit) then perhaps default L/Rs overall are too high (or conversely LDFs or trends too light)
If trend is up when going from e.g. 100k to 10mm att pt, then perhaps expos curve is predicting well at lower points but is underestimating upper points
22. 22 Test of Default Parameters (cont.) Before making overall judgments, must consider
UW contract selectivity (contracts seen vs. written),
Sample size (# of cedants/years),
Impact �as-if� data (either current or historical)
Survivor bias
Systematic bias in models
�Lucky�
23. 23 Test of Default Rating Factors � Example 1
24. 24
25. 25 Reinsurance Market Reinsurance business mix1 Europe US / Can
Property 46% 34%
Motor 21% 8%
Liability & WC 20% 35%
Other 3% 23%
Reinsurance type2
Proportional 70% 50%
Non-Proportional 30% 50%
P & C Reinsurance Demand3 $ 51 b $ 65 b
26. 26 Exposure Benchmarks Insurance business mix Europe US / Can
Property 24% 27%
Motor 38% 41%
Liability 10% 14%
WC 0% 11%
A&H 17% 2%
Other 11% 5%
27. 27
28. 28 Summary Weighting of alternative methods should be viewed as the actuarial equivalent of crying �uncle�.
Do not view weighting as a positive approach to coming up with an answer, but a concession that there are things going on you haven�t modeled
Perfectly acceptable if the only remaining differences are noise � if not, improve the model
29. 29 Appendices
More Advanced Puzzle Solving Techniques
Hybrid Steps
Credibility
One of the most difficult puzzle pieces
30. 30 Appendix - More advanced techniques for Solving the Puzzle Inspecting Experience/Exposure differences
31. 31 Appendix - More advanced techniques for Solving the Puzzle Pressure Indicators �years (or layers)
32. 32 Basic Steps of The Hybrid Method Step 1: Estimate Experience burns & counts
Select base attachment points/layers above the reporting data threshold
Estimate total excess burns using projection factors
Estimate excess counts using frequency trends, claim count LDFs
Calculate implied severities
Step 2: Estimate Exposure burns & counts
Use same attachment points/layers as Experience
Estimate total burns and bifurcate between counts, average severities
Step 3: Calculate Experience/Exposure frequency ratio by attachment point
Estimate overall averages using number of claims/variability
Step 4: Review frequency ratio patterns
Adjust experience or exposure models if needed and re-estimate burns (!!)
Select indicated experience/exposure frequency ratio(s)
Step 5: Similarly review excess severities and/or excess burns
Step 6: Combine Hybrid frequency/severity results
Using experience adjusted exposure frequencies and severities
Step 7: Determine overall weight to give Hybrid
33. 33 Estimation of Hybrid CountsPreview Steps 1 to 4 A: Select base attachment points above data threshold
Example: threshold=150k; reins layers=500x500k, 1x1mm
Select 200k, 250k, 350k, 500k, 750k, 1mm attachment points
B: Calculate experience counts
At lower attachment points, year by year patterns should be variable about some mean
For example, if upward trend, then perhaps:
Overdeveloping or trending later years
C: Calculate exposure counts for comparison
D: Review experience/exposure frequency patterns
Should be relatively stable until credibility runs out
Double back to methods if not
Select frequency ratios to estimate Hybrid counts
34. 34 Step 1a: Experience Counts and Burns Sublayer $150,000 xs 350,000
35. 35 Step 1b: Review Experience CountsYear Variability: >350,000 Attachment
36. 36 Step 1c: Review Experience CountsYear Variability: >1,000,000 Attachment
37. 37 Step 1-Recap: Estimation of Experience Burns, Counts and Implied Severities
38. 38 Step 2: Estimation of Exposure Burns Bifurcated Between Counts and Severities
39. 39 Step 3: Calculate Experience/Exposure Frequency Ratios and Base Layer Weights
40. 40 Step 4a: Review Exper/Expos FrequenciesAttachment Point Pattern: 200k�1mm
41. 41 Step 4-Recap: Select Exper/Expos Frequency Ratio For Hybrid Claim Count Estimate
42. 42 Step 5: Selected Severity
43. 43 Step 6: Selected Overall Hybrid Burn
44. 44 Classical Credibility Weighting Estimate separate Experience and Exposure burns
Select credibility weights using combination of:
Formulaic Approach
Expected # of Claims / Variability
Exposure ROL (or burn on line)
Questionnaire Approach
Apriori Neutral vs. Experience vs. Exposure
Patrik/Mashitz paper
Judgment
Need to check that burn patterns make sense
i.e. higher layer ROL < lower ROL
similar to Miccolis ILF consistency test
45. 45 Classical Credibility Weighting
46. 46 Assessing Credibility of Exposure Method Assess confidence in:
Exposure curve selected
Exposure profile
Source of hazard or sub-line information
Prediction of next years primary loss ratio
Percentage of non-modeled exposure, clash, etc.
Company strategy and ability to realize strategy
Possibly take questionnaire / scoring approach to mechanize (Patrik/Mashitz)
47. 47 Assessing Credibility of Experience Method Assess confidence due to:
Overall volume of claims
Volume of claims within layer (lucky or unlucky?)
Stability of year by year experience results
� layer to layer experience results
Source of loss development, trend factors, historical rate changes and deviations
Changes in historical profile limits
Appropriateness of any claims or divisions that may have been removed (or �as-if�d�)
Experience score compared to exposure score to determine credibility weight
48. 48 Increase Credibilityby Reducing Variability Above figure from iconic Philbrick CAS paper
In this case, A represents Experience rating average (with indicated process noise), while B represents Exposure
Goal will be to bring A and B closer together thereby reducing parameter variance, with any remaining difference being process noise