1. Reported Loss (a.k.a. case incurred loss)´╗┐
    Sum of paid loss and ending case reserve

    Reported Losses = Paid Losses + Case Reserve´╗┐
  2. Ultimate Loss
    • Amount required to settle all claims for a de fined group of policies
    • Diff ers 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
  3. Aggregated loss measures defi ned by
    • 1. Choice of relevant statistics (pd or rpt loss)
    • 2. Data aggregation method (CY, AY, PY)
    • 3. Period of time (Acctg period or Valuation date)
  4. Allocated loss adjustment expenses (ALAE)
    • Claim related expenses that can directly be attributable to a specifi c claim
    • E.g., legal fees for outside counsel hired to work on a specifi c claim
  5. Unallocated loss adjustment expenses (ULAE)
    • Claim related expenses that cannot directly be attributable to a speci c claim
    • E.g., claims department salaries and rent
  6. 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
  7. 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
  8. 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
  9. Report Year Losses
    • Group claims according to date of report to the insurer
    • Claims-made coverage is dependent on the report date
    • No IBNR
  10. 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
  11. Adjustments to Losses
    • To project to level expected when rates will be in eff ect
    • 1. Extraordinary Losses
    • 2. Changes in coverage or benefi t levels
    • 3. Loss Development
    • 4. Loss Trend
  12. What type of Extraordinary Losses are there?
    • 1. Large Individual Losses
    • Infrequent individual losses for extremely large amounts

    • 2. Catastrophic Losses
    • Events whose losses are very large and very infrequent s.t. including them in normal rate review would severly distort the estimation of future expected losses
  13. 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 (may be much higer than basic rate)
  14. When basic limit is not used, determine threshold that best balances the following goals
    • Include as many losses as possible
    • Minimize volatility in analysis
  15. 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)
  16. 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
  17. Describe the parts that go into total loss cost
    • Non-Cat (adjustments like normal losses)
    • +
    • Non-Modeled Cat (like Hail)
    • +
    • Modeled Cat (like Hurricanes)
    • = Total Loss Cost
  18. 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
  19. Number of years used for non-modeled cat analysis
    Should be selected based on both stability and responsiveness
  20. 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
  21. How can models be used to monitor concentration risk?
    • May choose to write less in CAT-Prone areas, get more reinsurance or write higher deds
    • May choose to alter UW Profit in rates to reflect higher cost of capital needed to support risk caused by higher concentration of policies
  22. Name the two types of Reinsurance
    1. Proportional reinsurance - same % of premiums & losses shared with reinsurer (No need to explicitly include in indications)

    2. Non-proportional reinsurance - reinsurer assumes some layer of losses
  23. Two ways to consider non-proportional 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
  24. Loss Development
    Project unpaid (often unreported) claims to ultimate settlement values
  25. 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
  26. 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
  27. 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
  28. Loss Trend
    Adjust data for changes in frequency and severity
  29. 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
  30. 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 eff ect (usually policy year)
  31. Two-Step Loss Trending
    • Used when expect trend in historical period and forecast period to be dffi erent
    • 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
  32. Leveraged Eff ect 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
  33. 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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