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Frequency Severity Techniques

Approaches

Approach #1

Develop claim counts. Develop severity. Multiply

  • Given
    • Counts
    • Severity ← Claim Amounts
  • Assume
    • Exposures are constant over time
  • Find
    • Ultimate claim counts
    • Ultimate severity
    • Ultimate claims
  • Gives you
    • Ultimate Claims

Approach #2

Just find the frequency and severity, using appropriate exposure information. Trend to the level for which the estimates need to be obtained. Develop frequency and severity to ultimate. And multiply these with the exposures of the subject period.

  • Given
    • Exposures (e.g. Payroll)
    • Claim counts
    • Severity ← Claim amounts
    • Trends
  • Assume
    • Exposures are constant over time
    • Trends are expected to continue in the future.
  • Find
    • Trended Frequency
      • = \(\dfrac{\text{Trended Ultimate Counts}}{\text{Trended Exposures}}\)
      • Exposures are already know as it is policy data
      • Counts have to be developed since they are experience data
    • Trended Ultimate Severity
  • Gives you
    • Ultimate Claims

Approach #3

Find the incremental severity and the incremental claim count, and multiply them together for each maturity. Sum them up to retrieve the ultimate claims. Be careful about cumulative vs incremental.

  • Given
    • Claim counts
    • Disposal rates ← Claim counts + Ultimate counts
      • Ultimate counts ← Rept counts
    • Incremental Severity ← Paid claims + Claim counts
    • Trends
  • Assume
    • Expect Disposal rates are relevant in future periods too
  • Find
    • Incremental counts between ages for future periods of the AY
      • \(\dfrac{\text{(Ult\# - Latest\#)}}{1 -\text{Latest DR}}\times (\text{DR}_{j+1} - \text{DR}_{j})\)
      • Note: no need to trend these counts… we are using the pattern
    • Trended Incremental Paid Severity for future periods of the AY
  • Gives you
    • Unpaid claims

Tail Severity

  • Considerations
    1. Combine data at the age at which results become erratic \(\implies\) more stability
    2. If the influence on the total projections, of selecting a particular age is very small. Then further more refined analysis may not be necessary.
    3. \(E(\text{\% of claims to be closed}|Age)\).
      • Enough claims should be there to provide a more stable severity estimate.
      • Not too many claims, since some should remain to provide estimates for earlier maturities where age-to-age factors are more stable.
  • Given
    • Incremental Amounts
    • Incremental Counts
    • Trends
  • Find
    • Trended incremental Amounts
  • Gives you
    • Tail severity at a certain AY level

Misc.

  • When doing volume weighted averages for severity
    • =SUMPRODUCT(P14:P15/O14:O15,D9:D10)/SUM(D9:D10)
    • Weight the severity LDF with the claim counts of the starting period.
  • Smaller periods?
    • Better recognition of seasonal development
    • Useful when average accident dates are changing over time.
  • Ignore the period where there is a temporary change, as that is not expeted to continue in the future.

Mistakes

  • Multiplying the severity dev factor by paid claims instead of severity.