Reserving Text Flashcards
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Describe 5 components of unpaid claims
1) Case outstanding (on known claims): this reserve is set by the claims department, third party adjustors, or independent adjustors for known and reported claims only (the future expected payments for claims already reported.
2) IBNER: a provision for future development on known (case) reserves (incurred but not enough reported).
3) Reopen: a provision for expected costs due to the reopening of claims.
4) IBNR: provision for claims incurred but not reported (this is the narrow definition of IBNR). IBNR comes about due the lag between a covered event occurring, and it being reported to the company—in some lines of business this time lag can be very long.
5) In transit: a provision for claims reported, but not yet recorded within the database/system.
How do you calculate incremental paid claims, case outstanding, and reported claims?
Incremental paid claims during a period are the sum of payments in the period, or equivalently cumulative paid claims at the end of the period minus cumulative paid claims at the beginning of the period.
Similarly, incremental case O/S changes during a period are the sum of changes in case O/S in the period, or case O/S at the end of the period minus case O/S at the beginning of the period.
Incremental reported claims within a period can be calculated in the following ways:
1) Reported claims at end of period – reported claims at beginning of period.
2) Incremental paid + case O/S at the end of period - case O/S at the beginning of period.
3) Incremental paid + incremental case O/S.
4) Sum of incremental reported claims during the period.
External data commonly used when (3):
1) Small company: data sets not credible.
2) Systems limitations limit availability of data.
3) Entering a new line of business or region.
External data is particularly useful as a benchmark for (3):
External information can be very valuable as a benchmark, especially for the following:
1) Tail development factors.
2) Trend rates.
3) Expected claims ratios.
External data may be misleading or irrelevant due to differences in (5):
External data may be misleading or irrelevant due to differences in:
1) Insurance products.
2) Case outstanding and settlement practices.
3) Insurer’s operations or coding.
4) Geographic areas
5) Mix of business/products
Consideration for data groupings for an unpaid claims analysis (6):
1) Volume of claim counts in the group.
2) Length of time to report the claim once an insured event has occurred- i.e. reporting patterns.
3) Ability to develop an appropriate case outstanding estimate from earliest report through the life of the claim- i.e. accuracy of case reserves.
4) Time to settle the claim once it is reported- i.e. settlement, or payment patterns.
5) Likelihood of claims to reopen once it is settled.
6) Average settlement value- i.e. severity. -Must balance credibility and homogeneity of groupings. If relative volume of business between two or more segments is constant, less homogeneity in groupings is needed.
Treatments of ALAE under excess of loss reinsurance (3):
1) ALAE included with claims in the limit.
2) ALAE not covered.
3) ALAE covered pro rata: i.e. covered in the same proportion as claims, e.g. if $5M of a $15M claim is covered, 1/3 of ALAE will be covered.
Examples of exposures used in estimating unpaid claims: (8):
1) Earned premium: most commonly used, on-level if available.
2) Written premium.
3) Policies in force.
4) Number of vehicles insured- auto.
5) Payroll- WC.
6) Property value- property insurance.
7) Number of employees- crime.
8) Sales- general liability.
Define the following: Policy effective dates Accident date Report date Accounting Date Valuation Date
Policy effective dates: policy begin and end dates.
Accident date: the date of covered occurrence.
Report date: date claim reported to the insurer.
Accounting date: the date through which liabilities are estimated, for all claims occurring on or before regardless if they have been reported or not.
Valuation date: the date through which known claim data is included, regardless of when the actuary performs the analysis.
Describe Calendar Year aggregation (including Advantages and Disadvantages)
Calendar Year (CY): payments include all claims paid in a given year regardless of when the accident, policy, or report of claim occurred. CY exposures (e.g. calendar year earned premium) are commonly used, but CY claims are rarely used to estimate unpaid claims. CY earned premium can be calculated as: WP + (Beginning Unearned Premium Reserve - Ending Unearned Premium Reserve).
Advantage: readily available and is not subject to further development. -
Disadvantage: cannot be used it to estimate development of claims.
Describe Accident Year aggregation (including Advantages and Disadvantages)
Accident Year (AY): by far the most commonly used aggregation for claims data. Claims are grouped by the year of occurrence, regardless of when the claim is reported, policy was written, or payments are made. Actuaries commonly use CY exposure data with AY claims data (CY exposures approximately match AY claims).
Advantage: Represents a shorter timeframe than policy years (or underwriting years) so we can estimate ultimate claims sooner, and there are numerous industry benchmarks available on an AY basis.
Disadvantages: slight mismatch with CY exposures, the potential for mixing of claims from policies underwritten/priced at differing levels, or at different retentions for self-insureds.
Describe Policy Year aggregation (including Advantages and Disadvantages)
Policy Year (PY) or Underwriting Year: Claims can be grouped by when the policy was written (PY if a primary policy, U/W year if a reinsurance policy) regardless of when claims occur, are reported, or paid. -
Advantages: PY claims directly match PY exposures, and are useful If there have been significant changes in policy characteristics or shifts in types of business written from one year to the next (since AY aggregation will mix claims from different PYs).
Disadvantages: the extended timeframe. it can also be hard to understand or isolate the effects of a large event (e.g. catastrophe). If a catastrophic event occurs in April, it will affect policies written in the prior year and current year (i.e. the effect will be spread over the current and prior PY).
Describe Report Year aggregation (including Advantages and Disadvantages)
Report Year (RY): Claims can be aggregated by the year claims are reported, regardless of when the claim occurred, are paid, or when the policy was in effect.
Advantage: number of claims is fixed by the end of the first year, resulting in more stable data.
Disadvantage: only measures development on case (IBNER) rather than newly reported claims (IBNR).
Sample Topics/Question with: Claims Department
Claims: understand any changes in claim settlement or report speed, changes in case adequacy (or how case reserves are set), shifts in large/small claims, or changes in the rigor of claims defense.
Sample Topics/Question with: Underwriting Department
Underwriting: understand shifts the book of business, large risks underwritten, and pricing of policies.
Sample Topics/Question with: Data/Accounting Department
Data or Accounting: understand changes in claim coding, data availability and definitions, and processes in place to ensure data accuracy.
Sample Topics/Question with: Ratemaking Actuaries
Ratemaking actuaries: understand any changes in operations, shifts in the book of business, use and availability of external data, filing information, and priced claims ratios.
Sample Topics/Question with: Reserving Department (if you are a consultant)
If you are a consultant and meeting with in house reserving actuaries, ask for prior reserve reports to review, ask about areas of disagreement between prior studies, and for any additional background they can provide.
Sample Topics/Question with: Reinsurance Department Senior Management
Reinsurance: details of the reinsurance programs, especially any changes in the program or retentions.
Sample Topics/Question with: Senior Management
Senior management: company overview, types of business written, types of marketing and distribution channels (e.g. direct writer, independent agents, captive agents), and any organization changes.
Describe the 3 important dimensions of the development triangle
Rows, the columns, and the diagonals.
Each row in the triangle represents one accident year.
Each column represents the age (or maturity) of development.
Each diagonal represents the values at each successive valuation date.
The sum of the latest diagonal minus the sum of the second latest diagonal represents the amount paid during that given timeframe since each valuation represents a cumulative value.
Explain how for self-insurers the policy year, fiscal year, and accident year are commonly the same
Self-insurers issue policies on a single date (rather than throughout the year as insurers do) and this date often corresponds to the first day in the fiscal year, and in these cases the accident year is defined over the same timeframe as the fiscal year (accident years do not necessarily have to run 1/1 to 12/31). In such a situation the policy year, fiscal year, and accident year would all be the same timeframe.
What should be considered when deciding on the number of periods to include in the data triangle?
Line of business, state, and type of data. Ideally, we would like to have development periods available until we expect no further development– often we will not have this amount of data and will need to use tail factors to project from the oldest maturity to ultimate.
What are 4 very basic diagnostic checks that should be done for claims amounts?
1) Visual examination of the Reported claims development triangle.
2) Visual examination of the Paid claims development triangle
3) Triangle of Reported Claims/Earned Premium (on-level if available).
4) Triangle of Paid Claims/ Earned Premium (on-level if available).
What diagnostic triangle is useful in looking for changes in case outstanding adequacy or settlement patterns?
The actuary can examine the consistency of paid claims to reported claims by looking at a triangle of paid to reported claims.
If case reserves are becoming more adequate the ratio would go down because case is contained in reported claims in the denominator.
If settlement patterns are increasing, we would expect the ratio to increase at earlier ages since more will be paid earlier and paid claims are in the numerator.
Since this diagnostic is a ratio, a change in either could be causing the differences, and no change in the ratio does not necessarily imply there are no changes in either as there could be offsetting changes in each.
When evaluating a diagnostic triangles what dimension are we generally looking at?
We are generally most interested in changes down columns– differences by AY at the same maturity indicting changes in development patterns.
What are 3 very basic diagnostic checks that should be done for claim counts?
1) Visual examination of the Reported claim count development triangle.
2) Visual examination of the Paid claim count development triangle
3) Triangle of Closed Counts/Reported Counts—Examining the ratio of closed counts to reported counts is a very useful metric which can indicate a change in the settlement rate of claims. Blips in this ratio can be caused by one time internal or external events (e.g. systems outages or catastrophes)— we are more interested in persistent changes or trends.
What are 3 diagnostic checks use averages? What information can we gain by comparing them?
1) Triangle of Reported Claims/Reported Counts (i.e. avg. reported = reported severities).
2) Triangle of Paid Claims/Closed Counts (i.e. avg. paid = paid severities).
3) Triangle of [Reported– Paid Claims] / [Reported -Paid Counts] (i.e. avg. case outstanding).
We are interested in comparing the trends down the columns of each. If things are steady trends would be fairly similar.
If case adequacy is increasing we would see higher trends in the average outstanding and average reported triangles than the average paid claims triangle.
We can also look for shifts within each, indicating a change in type of claim being settled at each age.
What the basic steps to complete the development technique? Why will the latest diagonal of the age-age triangle be blank?
1) Compile claims data in a development triangle (as covered in Chapter 5).
2) Calculate age-to-age factors (aka link ratios or report-to-report factors).
3) Calculate averages of the age-to-age factors.
4) Select claim development factors (CDFs).
5) Select a tail factor.
6) Calculate cumulative claim development factors.
7) Project ultimate claims.
Due to the shape of a data triangle, the triangle of age-to-age factors will have one less row and column than the data triangle (i.e., the latest diagonal will not have an age-age factor since the following period has not yet occurred).
What characteristics should the actuary look for when selecting claim development factors?
1) Smooth downward progression of age-age factors across development periods.
2) Stable age-age factors within development periods: in general, less mature age-age factors are often less stable– there should be no clear trends down columns, even at less mature ages (i.e. early volatility should be random).
3) Credibility of the experience: if the insurers own historical experience data is limited the actuary may use experience from similar lines with similar claims handling practices within the company, or use industry development factors.
4) Changes in patterns: review age-age factors for changes that may suggest changes in internal operations or external environment such as trends in age-age factors down the columns.
5) Applicability of historic patterns to the future: consider changes in the book of business, insurer operations, and external factors both observed in the historic period and those that may not have shown up in the claims experience yet.
3 approaches to estimate tail factors
1) Reliance on industry benchmarks.
2) Fit a curve to the selected (or observed) development factors.
3) If reported claims are assumed to be at ultimate value, use the ratio of reported to paid claims at the oldest age as the tail factor of the paid triangle (since reported claims are assumed to be at ultimate value, the ratio measures paid development to ultimate value). The reported tail will be 1.00 since it is assumed to be at ultimate already.
% Reported % Paid
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General observations and common relationships of the development technique
Claim development factors will generally be larger for the most recent (most immature) accident years and smaller for older (more mature) accident years. As a result, IBNR will often be largest in the most recent accident years. This makes sense because as the accident years mature more claims will be reported and paid, moving the IBNR and unpaid loss estimate closer to 0.
Development factors tend to increase as retentions (limits in the underlying data) increase because large claims tend to be reported later, thus at a higher retentions (limits) larger losses will be observed later in the triangle resulting in higher claims development factors.
As such, retention must be taken into consideration in estimating ultimate losses and deciding how to segment your data into triangles. Ignoring retentions will lead to errors in both reserving and ratemaking.
What is primary assumption of the development technique? Implicit assumptions when using paid and reported claims? When it is appropriate to use the development method?
Method assumes we can predict future claims activity based on historical claims activity to date by looking at how prior periods developed– primary assumption is that reporting and payment patterns will be similar going forward to patterns in the past. Using reported claims implicitly assumes there have been no significant changes in case adequacy levels during the experience period. Using paid claims implicitly assumes no material changes in speed of claim closure and payment. Appropriate for insurers in a relatively stable environment with no major organizational (e.g., new claims processing system) or external environmental (e.g., tort reform) changes. Requires a large volume of historical data, and works best when data is not distorted by large claims. The method works best with high frequency low severity claims. ? If assumptions do not hold, the actuary should consider alterative techniques (or at least adjust the selected claim development factors).
Additional implicit assumptions of the development method Advantages of the development method Disadvantages of the development method
The method also implicitly assumes a stable mix of claim types, stable policy limits and reinsurance retentions, consistent claims processing, and that claims are evenly spread throughout the periods being evaluated. Advantages: it is the most basic method, it works well if the book of business is stable, especially for low severity high frequency lines of business. The CDFs and claim estimates are inputs to many other methods. Disadvantages: is very susceptible to changes in the book of business or environment, and is very sensitive to claims reported (paid) to date (i.e., estimates are often highly leveraged).
3 examples of ways an actuary can set the a-priori ultimate claim estimate
1) Multiply the ratemaking expected claims ratio (ECR) by earned premium in the period.
2) Estimate expected claims using a complex simulation model requiring extensive expert input (No specifics are needed for the exam, this is just given as an example).
3) Estimate the claims ratios for each AY by developing, trending, and adjusting actual claims from each other AY for benefit level changes, then dividing by on-level earned premium. This is the method used in most of the examples in the text and tested the most.
3 situations the expected claims method is commonly used
1) When entering a new line of business or territory, therefore data is unavailable for other methods. 2) Historical data becomes irrelevant for projecting future claims, due to changes. 3) Very long tailed lines of business when the development factors are highly leveraged (high CDFs). 4) As an input to the BF method. Rsv. Chapter 8 – Expected Claims Technique
Describe the steps to complete the textbook expected claim technique
1) Develop an initial ultimate claim estimate—commonly the average of the paid and reported development estimates.
2) Adjust premium and claims to the target year cost levels (on-level premiums, trend and adjust claims for tort reform, trend exposure base if using something other than premium that is inflation sensitive).
3) Divide the adjusted claims by adjusted premiums to get claims ratios (CR) at the target years’ level—make a CR selection (exclude the data of the target year itself from the average you use for selection).
4) The expected claims method ultimate loss estimate (a-priori ultimate claims) for that AY are then the selected CR times earned premium.
5) Repeat for other immature AYs— CRs for mature AYs will often be selected judgmentally or together.
Advantage of the expected claims method Disadvantage of the expected claims method
Advantage: stability
Disadvantage: also stability, or more specifically lack or responsiveness—the actuary can make it more responsive by actively monitoring and updating the a-priori estimation as needed
What are the basic steps of the Bornhuetter-Ferguson Technique?
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Formulas for % unreported and % unpaid
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Assumptions of the BF method
The primary assumption of the reported BF method is that unreported claims will emerge in accordance with expected claims. Unreported claims are based entirely on expected claims, so the method assumes claims reported to date contain no information that can be used in predicting unreported claims (opposed to the expected claims method assumption that reported claims to date contain no information that can be used to predict ultimate claims).
How can the BF method be thought of as a weighted average?
XXXXXXXXXXXXXXXXXXXX Rsv. Chapter 9 – Bornhuetter-Ferguson Technique
What are two situations that could result in z>1.0 in the BF method, and what does the text recommend doing?
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Z>1.0 when CDF <1.0 which can occur due to Sub-Sal or conservative case reserves. The text recommends limiting the CDFs to ? 1.0 so that z?1.0
What are the basic steps of the Benktander method?
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Rsv. Chapter 9 – Bornhuetter-Ferguson Technique
Assumptions of the Benktander method What estimate does the Benktander method approach as iterations increase?
The Benktander method’s IBNR estimate blends actual and expected experience, compared to the BF IBNR estimate which is based entirely on expected claims (ignoring actual). The Benktander method gives more weight to actual claims than the BF, since the BF IBNR estimate ignores actual claims, while the Benktander IBNR estimate gives credit to the actual claims via the BF ultimate estimate. The Benktander method will approach the development technique estimate after sufficient iterations are performed (i.e. re-run the Benktander using the ultimate estimate from the first Benktander as the a-priori, and so on) since for each iteration the IBNR estimate will give more weight to the actual claims.
Rank the following methods in terms of stability: Development Expected Claims Bornhuetter-Ferguson Benktander
Expected Claims Method > Bornhuetter-Ferguson > Benktander > Development Technique
The rakings of responsiveness are just the opposite of the above rankings
What is Huge White’s question and 3 example solutions?
In his review of the original BF paper, Hugh White raises the following hypothetical question: You are trying to estimate unpaid claims and the reported portion of expected claims are higher than expected—should you:
1) Reduce IBNR by a corresponding amount because you believe the higher reported claims are a result of accelerated reporting or case strengthening and you don’t expect ultimate claims to change? This is equivalent to the expected claims method.
2) Leave the IBNR unchanged because you believe the increase is due to random fluctuations, so ultimate claims will increase by the additional amount reported, but IBNR is unaffected? This is equivalent to the BF method.
3) Increase the IBNR in proportion to the increase in reported claims because we believe the observed data is more predictive of future claims than our a-priori? This is equivalent to the development method.
How does each of the following methods perform under each of the following scenarios? Methods: Reported Development, Paid Development, Expected Claims, Reported BF, and Paid BF. Scenarios: Steady State, ? Claims Ratios, ? Case Adequacy, ? Payment Speed, ? Mix of Business
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Rsv. Chapter 9 – Bornhuetter-Ferguson Technique
In what ways are the Cape Cod and BF method similar and different?
The Cape Cod (CC) method (a.k.a. Stanard-Buhlmann) is very similar to the BF method, with the difference being the way we estimate the a-priori ultimate claims. The BF method a-priori uses the result of the expected claims method. The Cape Cod technique uses a mechanical, formulaic estimate. As such, the BF a-priori incorporates actuarial judgement where the CC apriori does not.
How does the Cape Cod method develop it’s a-priori ultimate claims?
XXXXXXXXXXXXXXXXXXXX Rsv. Chapter 10 – Cape Cod Technique
After developing the Cape Cod method’s a-priori ultimate claims, how do we estimate ultimate claims?
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Rsv. Chapter 10 – Cape Cod Technique
What is the primary assumption, advantages, and disadvantages of the Cape Cod method?
The primary assumption of the cape cod method is that unreported claims will develop based on expected claims, as calculated using reported claims and used up premiums. Advantages: the CC method uses reported claims in the calculation of the ECR, therefore it will respond (at least partially) to changes in claims ratios. As compared to the development technique, it is more stable (like the BF). Disadvantages: The CC is less appropriate than the BF if data is sparse or volatile because the ECR is formula driven, and not selected judgmentally as in the BF. It is also highly dependent on the availability and accuracy of the rate level adjustment factor (as is the expected claims method).
What is the primary difference between the frequencySeverity techniques and the other methods?
All of the methods we have examined thus far evaluate claims in aggregate. Frequency-Severity methods evaluate the frequency and severity of claims separately, providing insights into the drivers of claims development.
What is the primary difference between the frequencySeverity techniques and the other methods?
All of the methods we have examined thus far evaluate claims in aggregate. Frequency-Severity methods evaluate the frequency and severity of claims separately, providing insights into the drivers of claims development.
Describe the steps of performing the most basic F-S technique using counts and severities (Method #1)
Use the development technique to develop ultimate claim count and severity estimates. 1) We should develop both closed and reported claims, then select ultimate claim counts (select the average of the two unless there is good reason to exclude one, e.g. seasonality). 2) Develop reported severities (reported claims/claim counts) to ultimate (for method #1 the text only uses reported severities, but there is no reason you couldn’t also use paid severities and make a selection as we did with claim counts). 3) Ultimate claims = projected ultimate counts x projected ultimate severities.
Describe the steps and benefits of the F-S method that incorporated exposures and inflation (Method #2)
Method #2: recognizes that method #1 may be highly leveraged for the most recent years, so it provides an alternative estimate for the latest two years, using an exposure base and the prior year’s data trended and adjusted to current levels (then backed off to the 2nd most recent yr.).
1) Adjust the selected ultimate claim counts from Method #1 for trend to the level of the latest year, for all years except the latest two. Divide by the adjusted exposure base (on-level if premium, trended if other and inflation sensitive) to find the trended frequencies, make a selection for the target year, then trend back for second latest year.
2) Adjust selected ultimate severities (Method #2 uses both developed reported and paid severities, and makes a selection for ultimate severities) for trend and tort reform to the level of the target year, for all years except the latest two. Make a selection for the latest year, then trend/unadjust back for the second latest year.
3) Ultimate claims = selected frequency x exposure x selected ultimate severity, for each of the
Describe the steps of the F-S method that uses disposal rates (Method #3)
XXXXXXXXXXXXXXXXXXXX Rsv. Chapter 11 –Frequency-Severity Techniques
What are the assumptions of the F-S methods?
1) Claim counts and severities will continue develop as they have in the past. 2) Claim counts are defined consistently over time (e.g. claim v claimant, inclusion of CNP claims, or at minimum the mix is consistent). 3) Claim types are reasonably homogenous (or at minimum, the mix between non-homogenous claim types is consistent).
What are the advantages and disadvantage of the F-S techniques?
Advantages of the Frequency-Severity methods:
1) Gain valuable information on the claims process (e.g. settlement rates, severities).
2) Can use paid data, so independent of case outstanding (also a strength of any paid method).
3) Can explicitly reflect inflation, rather than assuming past patterns will properly reflect future inflation.
Disadvantages of the Frequency-Severity methods: 1) The estimate is highly sensitive to the inflation (trend) assumption.
Describe the steps to complete the Case Development method (Method #1)?
Start with the Case Outstanding and Incremental Paid triangles.
1) Calculate Incremental Paid to Beginning Case ratios—make selections for each age.
2) Calculate Case to Previous Case ratios—make selections for each age.
3) Use the selected Case/Previous Case ratios from Step 2 to fill in the bottom half of the Case O/S triangle.
4) Use the selected Incr. Paid/Begin. Case ratios from Step 1, multiplied by the Case O/S in Step 3 to fill in the bottom half of the Incremental Paid triangle.
5) Sum up the incremental payments to find the cumulative payments and ultimate claim estimate.
What are the assumptions, appropriate situations to use, advantages, and disadvantages of the Case Development method (Method #1)?
Assumptions: future claims are related consistently to claims already reported This method is most stable/appropriate when most claims are reported in the first year, so that it can more accurately measure the incremental paid to prior case ratio. If there are significant new reports in future periods, this ratio will not be as steady due to more moving pieces. This is because future payments include those included in prior case, but also payments on newly reported claims.
Advantages: useful when most claims are reported in the first year, or when evaluating report year triangles.
Disadvantages: most lines of business, on an AY basis, have significant reports after the first year. Additionally, there are no industry benchmarks to compare our selected ratios by age to, and these selections are not necessarily intuitive or something the actuary would have gained knowledge of through general experience. As a result, this method is not commonly used by actuaries.
What are reasonable values, or ranges of values, for the tail factors of each of the two triangles we use in the first Case Development method (Method #1)?
Case to prior case: we select a tail factor of 0.00, implying there are no case reserves after the latest age in the triangle which is the default selection in this method. If we had selected a tail factor greater than 0.00, there would be case reserves in the To Ult column, but that would not lead anywhere since it never becomes the prior case reserves in the next. Incremental paid to prior case: Our selection represents the percentage of case outstanding at the latest age that is ultimately paid out. As such, it could theoretical by any number>0, but something close to 1.0 is more realistic.
When is the second Case Development method presented in the text useful, and how do you perform it (Method #2)?
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Rsv. Chapter 12 – Case Outstanding Development Technique
When is an alternative formula that can be used to complete the second Case Development method, which is more intuitive (Method #2)?
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Rsv. Chapter 12 – Case Outstanding Development Technique
What is the advantage and disadvantages of the second Case Development method (Method #2)?
Advantage: we are able to develop an estimate of unpaid claims when the only piece of information we have is case outstanding (and industry CDFs).
Disadvantages: since this method is used when historical data and company CDFs are not available, we must use industry benchmarks which may prove to be inaccurate for the specific company. It may not be a good estimate for more recent years, if CDFs are highly leveraged. Additionally, any individual large losses contained in the case reserves may distort the projection.
What is the preferred solution when insurers have undergone changes in operations and procedures, or the environment has changed, according the Berquist and Sherman?
Our preference should be to treat the problem of changes in operations and procedures or the market environment through data selection or rearrangement. For example, if the insurer changes their case methodology, the actuary may place greater reliance on methods using paid claims data (because paid claims are unaffected by case reserves). If we cannot resolve the data issues through data selection or rearrangement Berquist and Sherman present two adjustments we can make.
What diagnostics can we perform to test for changes in case adequacy levels?
To detect changes in the adequacy level of case outstanding we should examine trends down the columns of triangles of average Case O/S, ratio of Paid/Reported Claims, average Paid Claims, and average Reported Claims. If case adequacy is increasing, we would expect the trends to be the largest in the Case O/S triangle, followed by Reported Claims triangle, then Paid Claims triangle, since Case reserves would be growing at a faster rate than inflation (or paid claims trend) alone. We would also expect to see the ratio of paid to reported claims decrease in the same locations of the triangle as the case adequacy increases.
Describe the steps to perform the B-S adjustment for changing case reserve adequacy
Adjusting for changing case adequacy:
1) Restate the average case outstanding triangle ((Rep. Claims-Paid Claims)/(Open Claim Counts)) by trending the latest diagonal back, using a trend rate based on average paid amounts. Now all points in the average case outstanding triangle are at the case adequacy level of the latest period (diagonal).
2) Calculate the Adjusted Reported Claims triangle as Unadjusted Paid Claims + Open Claim Counts x Adjusted Average Case Outstanding (where Open Claims Counts = Reported Claim Counts – Closed Claim Counts).
3) Perform the development method on the Adjusted Reported Claims triangle.
What is the advantage and disadvantage of the B-S adjustment for changing case reserve adequacy?
Advantage: restates the reported claims triangle so that the assumptions of the development method hold (i.e. case outstanding adequacy is consistent). Disadvantage: the adjustment is very sensitive to the trend selection.
What diagnostics can we perform to test for changes in settlement rates?
To detect changes in settlement rates, build a triangle of closed to reported claim counts, and examine the trends down each column—an increase in this ratio indicated claims are closing faster while a decrease indicates claims are closing slower. Berquist and Sherman observe closed claim counts are highly correlated with paid claims. This adjustment first adjusts the closed claim count triangle, and uses that to estimate the adjusted paid claims triangle.
Describe the steps to perform the B-S adjustment for changing settlement rates
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Describe the steps if there has been both a change in case adequacy and in settlement speed
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The paid claims triangle only needs to be adjusted for the change in settlement speed, as before. The reported claims triangle needs to be adjusted for both the change in settlement speed and case adequacy. To incorporate both adjustments we calculate the Adjusted Reported Claims triangle as: Adjusted Paid Claims + (Rep. Claim Counts – Adj. Closed Claim Counts) x Adj. Average Case O/S 2nd Adj. Step 3 2nd Adj. Step 2 1st Adj. Step 1 Rsv. Chapter 13 – Berquist-Sherman Techniques
Define Salvage and Subrogation, along with the lines of business they are generally associated with
In the event of a total loss, the insurer pays the insured the full amount of loss, but is entitled to the damaged property, which they can sell—this is salvage. Salvage is generally associated with property lines of business. Subrogation is any recovery by the insurer of amounts paid to a covered insured from a thirdparty responsible for the damage. Subrogation is generally associated with liability lines of business.
Describe the two methods described in the text to estimate ultimate Salvage and Subrogation
The first is to simply develop S&S triangles to ultimate using the development method. If the data is available, we would want to develop both reported S&S and received S&S triangles to ultimate (“paid” S&S, but the payment is to the insurer from the third party, so it is really a negative payment). The second method develops the ratio of Received Sub-Sal/Paid Claims, to ultimate. The selected ultimate Sub-Sal/Paid Claims ratios are then multiplied by our estimates of Ultimate Claims, resulting in estimates of ultimate Sub-Sal. The second is much more likely to be tested.
What are the advantages and disadvantage of the Sub-Sal estimate using ratios?
Advantages: the development factors are not as highly leveraged because we are using a ratio, and we can judgmentally select ultimate S&S ratios for recent years if they appear out of line.
Disadvantage: any error in our ultimate claim estimate will affect the accuracy of the unpaid Sub-Sal estimate.
What should we consider when evaluating claims gross and net of reinsurance?
We need to be aware of the implied relationships between gross, ceded, and net claims throughout the analysis, including at the beginning while reviewing and reconciling the data, during the analysis while preforming the methods, and at the end when making final ultimate claim selections across methods. The selections should be consistent with the reinsurance program(s) in place.
Describe how we can estimate expected reported and paid claims during a given timeframe
XXXXXXXXXXXXXXXXXXXX Rsv. Chapter 15 – Evaluation of Techniques
Describe two ways we can estimate the percentages (un)paid and (un)reported and when each is appropriate
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If our ultimate selections are based on the development method we can estimate the percentages using the selected CDFs, as done previously (i.e. %?????? = 1.0/????????? and %???????????????????? = 1.0 ? 1.0/?????????). Ultimate selections are rarely based only on the reported or paid development method—in such situations we may want to examine the ratios of paid and reported claims by age to selected ultimate claims, and make selections for reporting and payment patterns that way. Rsv. Chapter 15 – Evaluation of Techniques
Describe the methods described in the text to estimate ultimate ALAE
The text mentions we can use any of the methods discussed so far to estimate ALAE. In addition, the text examines two specifically. The first is simply the development method applied to ALAE. The second develops the ratio of Paid ALAE/Paid Claims to ultimate. The selected Paid ALAE/Paid Claims ratios are multiplied by selected ultimate claims, resulting in estimates of ultimate ALAE.
Describe the additive development method
The text presents the concept of the additive development method, to develop the ratio of Paid ALAE/Paid Claims. The additive development method uses additive age-age factors, and adds the cumulative CDF to the ratio on the latest diagonal, rather than multiplying them. The resulting CDF is multiplied by the current claims, as usual, to estimate ultimate claims.
What are the advantages and disadvantages of the ALAE estimation method that uses ratio?
Advantages:
1) Recognizes the relationship between ALAE and Claims.
2) The development factors are not as highly leveraged because we are using a ratio.
3) We can judgmentally select ultimate ALAE ratios for recent years if they appear out of line.
Disadvantages:
1) Any error in our ultimate claim estimate will affect the accuracy of the unpaid ALAE estimate.
2) Some lines of business may have large amounts of ALAE on claims that settle with no payment.
What unique challenges does estimating unpaid ULAE present?
Estimating unpaid ULAE presents a challenge because we have less information about the claims that are incurring these expenses since these expenses cannot be assigned to individual claims (i.e. since these expenses cannot be associated with an individual claim we do not know the AY and therefore don’t know the maturity either). Since ULAE cannot be allocated to individual claims, we cannot group ULAE by accident year—we can only observe calendar year payments of ULAE.
What are some items included in ULAE?
ULAE includes expenses such as general overhead, handling, administrative, and salary expenses of the claims department. Rsv. Chapter 17 – Estimating Unpaid ULAE
What is the market value of ULAE?
The fees a TPA would charge to take over the claims management of the current book of business. Self-insurers often set their unpaid ULAE estimate equal to this value.
What is the market value of ULAE?
The fees a TPA would charge to take over the claims management of the current book of business. Self-insurers often set their unpaid ULAE estimate equal to this value.
What is the primary difference in assumption between dollar based and count based ULAE methods?
Dollar based techniques assume ULAE tracks with claims, both in timing and amount while count based techniques assume ULAE is proportional to claim counts.
Explain the steps of the classical technique, including how it measures and applies the ULAE ratio
Classical Technique: calculate and select the ratio of CY Paid ULAE/CY Paid Claims. Apply selected ratio to 50% of Case O/S and 100% of IBNR. If given pure IBNR, apply 100% for pure IBNR only, and 50% to everything else (since everything else will have already been reported).
Explain the assumptions of the classical technique and when it is appropriate to use
The key assumptions of the classical technique are:
1) The ratio of paid ULAE to paid claims has reached the steady state (i.e. it won’t change in the future).
2) One half of ULAE is incurred when opening a claim, and the other half when closing a claim.
3) ULAE on unreported claims is proportional to IBNR and ULAE on open claims is proportional to case reserves. The classical technique is inaccurate if volume is growing or declining, if there is inflation, or if evaluating a long-tailed line of business. It will only give good results for very short tailed and stable lines of business (since paid claims will be approximately equal to reported claims).
Explain the steps of the Kittel refinement (to the classical technique), including how it measures and applies the ULAE ratio
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The classical assumption that paid claims are approximately equal to reported claims is unlikely to hold. The Kittel refinement assumes ULAE is incurred when the claim is reported, regardless if a payment is made, so it includes reported claims information. We calculate and select the ratio based on CY Paid/Average(CY Paid Claims & CY Incurred Claims) where CY incurred = CY paid + ? case + ? IBNR. We apply the selected ratio in the same way as the classical technique; 50% to case and 100% to IBNR (or 100% to pure IBNR and 50% to everything else, if a pure IBNR estimate is available). Rsv. Chapter 17 – Estimating Unpaid ULAE
Explain the steps of the generalized Kittel (Conger & Nolibos), including how it measures and applies the ULAE ratio
XXXXXXXXXXXXXXXXXXXX Rsv. Chapter 17 – Estimating Unpaid ULAE
Describe the three ways the generalized Kittel method estimates unpaid ULAE after selecting the ULAE Ratio
There are three ways this method estimates unpaid ULAE:
1) Expected Claims Method:
ULAE Ratio x Ultimate Claims – Sum of Paid ULAE.
2) BF Method:
ULAE Ratio x (Ultimate Claims – Sum of Claims Basis).
3) Development Method:
(Ultimate Claims/Sum of Claims Basis – 1.0) x Sum of Paid ULAE.
Describe the simplification of the generalized Kittel, including why it is useful in practice and how it measures and applies the ULAE ratio
XXXXXXXXXXXXXXXXXXXX Rsv. Chapter 17 – Estimating Unpaid ULAE
Describe the Mango-Allen refinement to the classical technique
If the actual historical CY claims are volatile, we can simply use expected CY paid claims in place of actual CY paid claims in the classical technique. Rsv. Chapter 17 – Estimating Unpaid ULAE
Describe the generalized approach to claim counts, including how the ULAE ratio is measured and applied
XXXXXXXXXXXXXXXXXXXX Rsv. Chapter 17 – Estimating Unpaid ULAE
Briefly describe the count based models proposed by the following: a) Wendy Johnson b) Rahardjo c) Spalla d) Mango-Allen e) R.E. Brian
a) Wendy Johnson: the generalized approach to claims counts with relative weights of v1 = 2.0, v2 = 1.0, and v3 = 0.0
b) Rahardjo: recommends incorporating duration into the calculation,
c) Spalla: use modern systems to track the time spent on various activities performed by the claims department, and use that more detailed information to perform a more detailed analysis of unpaid ULAE.
d) Mango-Allen: use open, closed, and pending (OCP) claims to predict future staffing levels, thus future adjustment costs.
e) R.E. Brian: an early count based method giving equal weight to opening a claim, maintaining a claim, making a single payment, closing a claim, and reopening a claim.
In what way is insurance fundamentally different than most other products? What is the actuary’s role in this difference?
Insurers do not know the true cost of the product they sell until many years after it is sold (or in some cases decades). Despite the ultimate value of these claims not being known for many years the insurance companies must report their financial results, including unpaid claim and claims expense liability estimates. It is the actuaries job to estimate these unpaid claims and expenses.
In addition to producing accurate financial reports, the accurate estimation of unpaid claims is important to what groups? Explain why accurate unpaid claim estimates are important to each
1)Internal managers: accurate estimates of unpaid claims are crucial for proper decision making in pricing, underwriting, strategical, and financial decisions. Ultimate loss estimates are used in ratemaking, so understated ultimate losses would lead to insufficient rate levels (and visa-versa). Inaccurate rates can cause significant issues for insurers— insolvency if rates are insufficient (especially if growing) or loss of market share if rates are redundant. Inaccurate estimates can also effect decisions on where to increase/decrease business written, reinsurance purchasing decisions, and capital management.
2)Investors: financial statements are relied upon by investors in making their investment decisions.
3)Insurance Regulators: rely on financial statements in making regulatory decisions. If reserves are understated, masking the true financial position, the regulator may be too late in reacting to a distressed insurer.
