W&M Ch 6 Flashcards
Ultimate Loss
- Amount required to settle all claims for a defined group of policies
- Differs from reported loss due to IBNR and case inadequacy or (IBNER)
- IBNER - incurred but not enough reported or development on known claims
Ultimate Losses = Reported Losses + IBNR Reserve + IBNER Reserve
Reported Loss (aka case incurred loss)
Sum of paid loss and ending case reserve
Reported Losses = Paid Losses + Case Reserve
Allocated loss adjustment expenses (ALAE)
- Claim related expenses that can be directly attributed to a specific claim
- e.g legal fees for outside counsel hired to work on a specific claim
Aggregated loss measures defined by
- Choice of relevant statistics
- Data aggregation method
- Period of time
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
Unallocated loss adjustment expenses (ULAE)
- Claim related expenses that cannot be directly attributed to a specific claim
- e.g. claims department salaries and rent
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
Accident Year Losses
- Losses grouped according to date of occurrence, regardless of when policy 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
Report Year Losses
- Group claims according to date of report to the insurer
- -Claims-made coverage is dependent on the report date
- No IBNR
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
When basic limit is not used, determine threshold that best balances the following goals
- Include as many losses as possible
- Minimize volatility in analysis
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
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)
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
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
Number of years used for non-modeled cat analysis
Should be selected based on both stability and responsiveness
Catastrophe models
Generallly used for projecting extremely sporadic, high severity events
- Stochastic models to estimate likelihood of events with varying magnitude
- -estimate damages resulting from events given characteristics of insured properties
- Catastrophe provision added to non-cat loss amount to get aggregate expected losses
Loss Development
Project unpaid (often unreported) claims to ultimate settlement values
Chain Ladder Method
- Future claims’ development is similar to prior years’ development
- Claims recorded to date will continue to develop in a similar manner in the future
- Past is indicative of the future
Mechanics of Loss Development
- Compile loss data in a development triangle
- Calculate age-to-age factors (aka report-to-report factors or link ratios)
- Calculate averages of the age-to-age factors
- Select loss development factors
- Select tail factor
- Calculate cumulative loss development factos
- Project ultimate claims
Other Methods for Calculating Loss Devlopment
- Bornhuetter-Ferguson Method
- Unreported (or unpaid) claims will develop based on expected claims - Berquist-Sherman Method
- Deals with changes in claims settlement rates or case reserving philosophy
Loss Trend
Adjust data for changes in frequency and severity
Examples of loss trend drivers
- Monetary inflation
- Increasing medical costs
- Advancements in safety technology
- Distributional changes in the book of business
- Social Influences, such as
- -changes in claim consciousness
- -court practices
- -legal precedents
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)
Two-Step Loss Trending
- Used when expect trend in historical period and forecast period to be different
- 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
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
Overlap Fallacy: Loss Development and Loss Trend
- Has been incorrectly suggested that severity trend is double counted when both loss development factors and severity trend factors applied to losses
- Both necessary
- Trend factor reflects trend between midpoint of experience period and midpoint of exposure period
- The LDF reflects trend between occurrence and settlement
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
