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Reported Loss (a.k.a. case incurred loss)
Sum of paid loss and ending case reserve
Reported Losses = Paid Losses + Case Reserve
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Ultimate Loss
- Amount required to settle all claims for a defined group of policies
- Differs from reported loss due to IBNR and case adequacy (or IBNER)
- IBNER - incurred but not enough reported or development on known claims
Ultimate Losses = Reported Losses + IBNR Reserve + IBNER Reserve
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Aggregated loss measures defined by
- 1. Choice of relevant statistics
- 2. Data aggregation method
- 3. Period of time
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Allocated loss adjustment expenses (ALAE)
- Claim related expenses that can directly be attributable to a specific claim
- E.g., legal fees for outside counsel hired to work on a specific claim
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Unallocated loss adjustment expenses (ULAE)
- Claim related expenses that cannot directly be attributable to a specic claim
- E.g., claims department salaries and rent
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Calendar Year Losses
- CY paid losses include payments made on any claim during calendar year
- CY reported losses equal paid plus change in case reserves
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Accident Year Losses
- Losses grouped according to date of occurrence, regardless of when pol written or claim reported
- AY paid losses include all payments made on claims that occurred in that AY
- AY reported losses include all payments plus ending case reserves for claims occurred in AY
- Accident year losses can change in successive calendar years
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Policy Year Losses
- Group losses by year in which policy was written
- Directly matches premiums and claims from a block of policies
- Paid and reported loss calculated similar to AY
- Policy year losses can change in successive calendar years
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Report Year Losses
- Group claims according to date of report to the insurer
- Claims-made coverage is dependent on the report date
- No IBNR
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Loss ratio
Measures the portion of each premium dollar needed to pay loss
- Projected Ultimate Loss and ALAE ratio:
- Ultimate Loss Projected to Future Level / Projected Earned Premium at CR
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Adjustments to Losses
- To project to level expected when rates will be in effect
- 1. Extraordinary Losses
- 2. Changes in coverage or benefit levels
- 3. Loss Development
- 4. Loss Trend
- How to determine threshold at which losses should be capped?
- Often capped at basic limits
- Ideally should correspond to point at which inclusion causes volatility in rates
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When basic limit is not used, determine threshold that best balances the following goals
- Include as many losses as possible
- Minimize volatility in analysis
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When excluding shock losses, must add back provision for shock losses
- Typically use average expected large loss calculated using many years of data
- Length of time depends on size of insurer and line of business
- Note - older data may be less relevant (e.g., changes in jury awards)
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Catastrophe Losses
- Event whose losses are very large and very infrequent such that their inclusion in a normal rate review would severely distort the estimation of future expected losses
- E.g., hurricane, earthquakes, oil spills
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Non-modeled cat analysis
- Generally used on events that happen with some regularity
- E.g., hail storms for auto physical damage
- If not treated separately, increase indicated rate need in years after events and understate needed rate in years without events
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Number of years used for non-modeled cat analysis
Should be selected based on both stability and responsiveness
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Catastrophe models
- Generally used for projecting extremely sporadic, high severity events
- Stochastic models to estimate likelihood of events with varying magnitude
- Estimate damages resulting from events given characteristic of insured properties
- Catastrophe provision added to non-cat loss amount to get aggregate expected losses
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Two ways to consider reinsurance in ratemaking analysis
- Reduce projected losses for reinsurance recoveries and premiums for cost of reinsurance
- Net cost of non-proportional reinsurance may be included as an expense item
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Loss Development
Project unpaid (often unreported) claims to ultimate settlement values
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Chain Ladder Method
- 1. Future claims' development is similar to prior years' development
- 2. Claims recorded to date will continue to develop in a similar manner in the future
- Past is indicative of the future
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Mechanics of Loss Development
- 1. Step 1 - Compile loss data in a development triangle
- 2. Step 2 - Calculate age-to-age factors (a.k.a. report-to-report factors or link ratios)
- 3. Step 3 - Calculate averages of the age-to-age factors
- 4. Step 4 - Select loss development factors
- 5. Step 5 - Select tail factor
- 6. Step 6 - Calculate cumulative loss development factors
- 7. Step 7 - Project ultimate claims
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Other Methods for Calculating Loss Development
- 1. Bornhuetter-Ferguson Method
- Unreported (or unpaid) claims will develop based on expected claims
- 2. Berquist-Sherman Method
- Deals with changes in claims settlement rates or case reserving philosophy
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Loss Trend
Adjust data for changes in frequency and severity
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Examples of loss trend drivers
- Monetary inflation
- Increasing medical costs
- Advancements in safety technology
- Distributional changes in the book of business
- Social Iflnuences, such as changes in claim consciousness, court practices, legal precedents
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Loss Trend Periods
Period of time from average loss occurrence date of experience period (usually cal/acc year) to average loss occurrence date for period in which rates will be in effect (usually policy year)
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Two-Step Loss Trending
- Used when expect trend in historical period and forecast period to be dffierent
- Legislative changes
- 1. Trend losses from average occurrence in experience period to average accident date in last data point in trend data
- 2. Trend from average accident date of last data point to average accident in forecast period
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Leveraged Effect of Limits on Severity Trend
- Assuming a constant percentage trend acting on all sizes of loss
- Basic limit losses will trend at a lower rate than losses limited at higher limits
- Which in turn trend at a lower rate than excess layers
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Overlap Fallacy: Loss Development and Loss Trend
- 1. Has been incorrectly suggested that severity trend is double counted when both loss development factors and severity trend factors applied to losses
- 2. Both necessary
- Trend factor reflects trend between midpoint of experience period and midpoint of exposure period
- The LDF reflects trend between occurrence and settlement
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