1
Q
3 Importance of Accurately Estimating Unpaid Claims
A
- Internal management: The estimates are used to make business decisions and underwriting. Inaccurately high estimates can lead to raising rates, tightening underwriting guidelines, exiting a business, or purchasing additional reinsurance.
- Investors: The estimates impact the profitability of the insurer. Inaccurately high estimates would lower the profit, making it appear like a worse investment.
- Regulators: The estimates are used to monitor the solvency of the insurer. Inaccurately high estimates resulting in a low profit might cause a regulator to restrict the insurer’s ability to write new business.
2
Q
5 Components of Unpaid Claims (also known as the Total Claims Reserve)
A
- Case reserves
- Provision for development on known claims (IBNER Reserve)
- Reopened claims reserve (IBNER Reserve)
- Provision for claims incurred but not reported (pure IBNR, IBNR Reserve)
- Provision for claims in transit (Incurred and reported but not recorded, IBNR Reserve)
3
Q
Chain Ladder assumptions
A
- Development of future claims will be similar to prior periods
- Claims observed for an immature period tell something about claims yet to be observed
4
Q
5 Diagnostic Triangles and what they tell
A
- Closed claim counts divided by reported claim counts: speedup/slowdown in closing claims
- Closed without pay claim counts divided by closed claim counts: higher/lower percentage of claims are being closed without pay
- Average paid on closed claims: severity trends, speedup/slowdown in closing small claims relative to large claims
- Average case reserves: severity trends, speedup/slowdown in closing, changes in case adequacy
- Paid losses divided by reported losses: speedup/slowdown in closing claims and changes in case adequacy
5
Q
Chain Ladder - Impact for change in settlement rates, change in case adequacy, changes in LR/Freq/Sev, Exposure Growth, change in product mix
A
- Change in settlement rates: reported would be unaffected, paid would under/overestimate
- Change in case adequacy: reported would be affected, paid would be unaffected
- LR/Freq/Sev: Unaffected for both reported and paid
- Exposure Growth: Unaffected for both assuming there is no change to the average accident date
- Change in product mix: Affected for both
6
Q
Expected Claims Method Ultimate formula
A
Ultimate = Expected Claim Ratio * EP Ultimate = Expected Pure Premium * Earned Exposures
7
Q
Expected Claims Method Assumptions
A
- Ultimate claims can be better estimated based on an a priori estimate than using the experience observed.
- Reasonable expected claim ratio can be obtained.
8
Q
Expected Claims Method - Impact for change in settlement rates, change in case adequacy, changes in LR/Freq/Sev, Exposure Growth, change in product mix
A
- Change in settlement rates: unaffected assuming ECR is not impacted
- Change in case adequacy: unaffected assuming ECR is not impacted
- LR/Freq/Sev: Inaccurate
- Exposure Growth: Unaffected on its own
- Change in product mix: Affected if the business that is changing has a different ECR
9
Q
BF Ultimate Formula
A
BF Ultimate = Actual Reported + EP * ECR * % Unreported
10
Q
Benktander Ultimate Formula
A
Benktander Ultimate = Actual Reported + BF Ultimate * % Unreported
Benktander gives more weight to development technique.
11
Q
BF Method Assumptions
A
- Unreported or unpaid claims will develop based on expected claims.
- A reasonable expected claim ratio can be obtained.
12
Q
BF Method - Impact for change in settlement rates, change in case adequacy, changes in LR/Freq/Sev, Exposure Growth, change in product mix
A
- Change in settlement rates: estimates still accurate for reported, paid would be inaccurate
- Change in case adequacy: paid will be accurate, reported will not be accurate
- LR/Freq/Sev: Not fully accurate
- Exposure Growth: unaffected on its own assuming average accident date is the same
- Change in product mix: affected if new business have different development pattern or ECR
13
Q
Cape Cod Ultimate Formula
A
CC Ultimate = Actual Reported + OLEP * ECR * % Unreported
CC ECR = sum(Reported claims) / sum(OLEP * % Reported)
14
Q
“Used up premium” formula
A
sum(OLEP * %Reported)
15
Q
CC Method Assumptions
A
- Unreported claims will develop based on expected claims, where expected claims are always derived using reported claims and earned premium.
- Claims reported and paid to date do provide some information about IBNR.
16
Q
Cape Cod ECR by AY trending backwards
A
year prior ECR = current year ECR * (premium trend factor / loss trend factor)
17
Q
CC Method - Impact for change in settlement rates, change in case adequacy, changes in LR/Freq/Sev, Exposure Growth, change in product mix
A
- Change in settlement rates: still accurate for reported CC
- Change in case adequacy: reported will be inaccurate, error will be more than BF but not as much as development
- LR/Freq/Sev: more accurate than BF
- Exposure Growth: unaffected on its own assuming average accident date is the same
- Change in product mix: affected if new business have different development pattern or ECR
18
Q
3 Different Approaches for Frequency - Severity Technique
A
- Using the development technique on claim count and severities separately
- Incorporating exposures and inflation to estimate highly leveraged years
- Disposal rate technique
19
Q
Frequency Severity Technique assumptions
A
- Claim counts and severities will continue to develop in future periods as they have in past periods.
- Consistent definition of claim counts throughout the experience period
- The mix of types of claims is relatively homogenous.
- (Disposal technique only) There are no significant partial payments.
20
Q
F-S technique #1 steps
A
- Start with claim counts and severity triangles.
2. Calculate LDFs separately and calculate ultimate claims by multiplying ultimate claim counts to ultimate severity.
21
Q
F-S technique #2 steps
A
- Start with exposure, counts, and severity by AY.
- Exclude the most recent year and calculate trended ultimate counts by AY.
- Calculate trended frequency by dividing trended ultimate counts by trended exposures. Select frequency to be used.
- Next calculate trended ultimate severity by AY. Select severity to be used.
- Calculate ultimate claims by multiplying selected frequency and selected severity.
22
Q
F-S technique #3 steps
A
- Start with cumulative closed claim count triangle with ultimate counts and an INCREMENTAL paid severity triangle
- Calculate disposal rates
- Project incremental closed claim counts using the selected disposal rates
- Trend incremental paid severity and select severity to be used
- Project unpaid claims using steps steps 3 and 4.
23
Q
Tail severity considerations
A
- Combine data at which results become erratic, since combining the data may provide more stability
- The influence on the total projections of selecting a particular age.
- Enough claims should be there beyond the selected age to provide more stability but not too many claims since some should remain to provide estimates for earlier maturities.
24
Q
2 Different approaches to Case Outstanding Technique
A
- Estimate future incremental payments using an insurer’s own triangle to obtain paid-on-case and remaining-in-case ratios.
- Use a reported and paid CDF to come up with a single factor to estimate total unpaid claims for an AY.
25
Case OS technique assumptions
1. Development of future claims will be similar to development in prior periods.
2. Case outstanding to date provides useful information about future claims development.
26
Case OS technique advantages
- When looking at report year triangles
- For claims made triangles, since there is no pure IBNR
- When looking at AY triangles, but nearly all claims are reported by the first column of the triangle
- Case OS #2 is useful when only current case OS data is available and other techniques cannot be used
27
Case OS technique disadvantages
- In most LOBs, case OS do not provide sufficient information about pure IBNR.
- There is a lack of industry benchmark data for AY applications.
- It is not intuitive.
- The projections can be distorted by large case reserves.
- The 2nd approach depends on industry CDF data so that might not be appropriate
28
Case OS Technique #1 steps
1. Start with case OS and Incremental paid triangles.
2. Calculate remaining in case ratios and select the ratios.
3. Use the selected ratios to project the rest of the Case OS triangle.
4. Calculate incremental paid on case triangle by dividing incremental paid by the prior case. Select ratios.
5. Use these selected ratios to project the rest of incremental paid triangles.
29
Case OS Technique #2 steps
1. Calculate the case OS dev factor.
= (1 - 1/PaidCDF) / (1/ReptCDF - 1/PaidCDF)
2. Unpaid claims = latest case OS * case OS dev factor
30
What Berquist-Sherman techniques can be used for
1. Adjusting triangles for changes in claim settlement rates
| 2. Adjusting triangles for changes in case reserve adequacy
31
Paid B-S technique assumptions
1. Changes in disposal rates are due to speedups or slowdowns in settlement rates, and not due to things like changes in the reporting patterns.
2. Higher disposal rates are associated with a higher percentage of ultimate paid claims.
32
Reported B-S technique assumptions
1. Any differences between the annual changes in average case reserves at each maturity and the severity trend are due to changes in case adequacy and not due to large unpaid claims.
33
B-S settlement rate adjustment steps
1. Start with cumulative closed claim counts triangle with ultimate counts and cumulative paid claims.
2. Calculate the disposal rate triangle.
3. Using the latest diagonal as the selected disposal rates, adjust the cumulative paid claims triangle.
3. 1. If disposal rate is higher than selected, adjusted paid = previous period paid + (current paid - previous paid)* (selected disposal rate in the column - previous disposal rate)/(current disposal rate - previous disposal rate)
3. 2 If disposal rate is lower than selected, adjusted paid = current paid + (next paid - current paid) *(selected disposal rate in the column - current disposal rate)/(next disposal rate - current disposal rate)
4. Perform development method in adjusted paid triangle to estimate ultimate claims.
34
B-S case adequacy adjustment steps
1. With the given triangles, calculate average cumulative paid severity.
2. Calculate % change by looking down a column. (severity trend)
3. Calculate average case outstanding triangle by dividing case OS by open claim counts.
4. Calculate % change by looking down a column. (case adequacy trend)
5. Assuming the change is due to a change in case adequacy, construct an adjusted average case OS triangle by keeping the latest diagonal as is and de-trending using severity trend from step 2.
6. Next construct an adjusted reported claims triangle by multiplying the adjusted average case reserves times the open claim counts and adding the cumulative paid claims.
7. Finally, perform reported development method and calculate ultimates.
35
How to perform both settlement rate and case adequacy adjustments
Adjusted Reported = (Adj open claim count * Adj avg case reserve) + adj cumulative paid claims,
where adj open claim count = reported claim counts - adjusted closed claim counts (based on selected disposal rates)
36
Reasons for reviewing unpaid claims estimates
1. Unpaid claims estimate should be updated if there has been a change in exposures.
2. To see if claims are developing as expected as a diagnostic check. Comparing actual development with expected development is called retroactive testing.
37
3 Options an actuary can take if a retroactive test revealed if actual development was above expected development
1. Reduce the IBNR. For example, this might be appropriate if there was a speedup in reporting.
2. Leave the IBNR unchanged. For example, this might be appropriate if there was a large reported claim.
3. Increase the IBNR. For example, this might be appropriate if there was a deterioration in the claim ratio.
38
Expected Emergence formula
Expected Reported Claims between t and t + 1 = (Estimated Ultimate Claims at t - Cumulative reported claims at t) * (%Reported_(t+1) - %Reported_t) / (1 - % Reported_t)
39
2 Approaches to estimating S&S recoverables
1. Use the development technique on a S&S triangle directly
| 2. Use a ratio approach that develops ratios of S&S to gross paid claims
40
Advantages of the ratio approach to estimating S&S
1. The development factors for the ratio approach tend to be less leveraged than the development factors based on received S&S dollars.
2. The ratio approach produces ratios of ultimate S&S to ultimate claims, which can be used as a diagnostic. If a ratio for a particular year seems unreasonable, a more reasonable S&S ratio can be selected for that year.
41
Ratio Approach steps for estimating S&S
1. Start with gross cumulative paid claims triangle and cumulative received S&S triangle.
2. Calculate the ratio triangle by dividing the 2 triangles.
3. Develop both paid claims triangle and ratio triangle to ultimate.
4. Ultimate recoverable S&S = ultimate paid claims * ultimate S&S ratio
42
3 Types of Reinsurance
1. Quota Share: Insurer cedes a constant percent of all claims to the reinsurer. 70% quota share means 70% is retained.
2. Excess of Loss (XOL): insurer will cede all amounts above a certain retention up to a certain limit on individual claims.
3. Stop Loss Treaty: Insurer will cede all amounts above a certain retention and up to a certain limit on the aggregate loss amounts. Stop loss "limit" is the retention at which the stop loss kicks in.
43
The relationship between tail of gross loss triangle vs. net or ceded loss triangle - for QS and XOL/Stop Loss
- QS: tail factors for gross/net/ceded triangles would be the same since it's just a constant multiple.
- XOL/Stop Loss: the tail factor for the ceded triangle will be larger than the gross triangle since once the retention is hit, all development occurs in the ceded layer.
44
3 Approaches to estimate ALAE
1. ALAE can be combined with claims to estimate claims and ALAE together. However, this ma not be a good idea if ALAE has a different development pattern.
2. Use the development technique on ALAE triangle directly.
3. Use a ratio approach that develops ratios of paid ALAE-to-paid claims. This assumes that the relationship between ALAE and claims is stable over the experience period.
45
Advantages of ratio approach for estimating ALAE
1. It recognizes the inherent relationship between claims and ALAE.
2. The development factors for the ratio approach tend to be less leveraged than the development factors based on ALAE dollars.
3. The ratio approach produces ratios of ultimate ALAE to ultimate claims, which could be used as a diagnostic.
46
Disadvantages of ratio approach for estimating ALAE
1. For some LOBs, there may be claims with no claim payment but substantial ALAE.
2. An error in the estimation of ultimate claims will lead to an error in the estimation of ultimate ALAE.
47
Advantage of the additive approach for estimating ALAE
It is more stable if the ratios are very small at early maturities
48
Ratio Approach for estimating ALAE steps
1. Start with cumulative paid triangle and cumulative paid ALAE triangle
2. Calculate the ratio of paid ALAE to paid claims triangle by dividing the two.
3. Develop using either a additive approach or a multiplicative approach.
4. Estimate ALAE by multiplying the CDF from step 3 to the ultimate paid claim.
CAS Exam 5
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