G.3. BF Method Flashcards
BF formula for estimated ultimate claims using paid data
BF Ultimate = Actual Paid + Expected Unpaid
= Actual Paid + Expected Claims x % Unpaid
= Actual Paid + EP x ELR x % Unpaid
BF formula for estimated ultimate claims using reported data
BF Ultimate = Actual Reported + Expected Unreported
= Actual Reported + Expected Claims x % Unreported
= Actual Reported + EP x ELR x % Unreported
How BF is credibility weighting of other methods
BF Ultimate = Development Ultimate x 1/CDF + Expected claims x (1 - 1/CDF)
Benktander formula
Benktander ultimate = Actual + BF Ultimate x % Unreported
How Benktander is credibility weighting of other methods
Benktander = Development Ultimate x 1/CDF + BF x (1 - 1/CDF)
Many iterations of Benktander
More weight to development ultimate until it approaches the development ultimate
Assumptions of B-F method
IBNR or unpaid claims are better estimated using a priori estimate. Claims reported to date tell you no useful information about IBNR or unpaid claims for that exposure period
Common uses of B-F
Random fluctuations or large claims at early maturities
When entering new line of business
Estimating ultimates at early maturities for long-tailed lines where early LDFs are highly leveraged
Advantages of BF and Benktander
B-F: more stable estimates than chain ladder and more responsive than expected claims
Benktander: even more responsive than B-F but still more stable than chain ladder (but not more stable than BF)
2 challenges in using BF or Banktander
- Estimating expected claims
2. Estimating expected % unreported
When credibility interpretation of BF and Benktander does not hold
Negative development, since 1/CDF > 1
Options for dealing with downward development using BF or Benktander
Continue to use
Limit CDFs to minimum of 1
Rely on different technique to select ultimates with CDF
Speedups/slowdowns and BF
Speedup: Paid will overestimate if speedup. Error will not be as big as chain ladder, since weight given to expected claims technique reduces amount of error
Case reserve adequacy and BF
Increase: reported will overestimate. Error will not be as big as chain ladder, since weight given to expected claims technique
Changes in claim ratios and BF
Do not fully react to changes in claims ratios due to Expected claims. Reported BF will be more responsive than Paid BF since more weight will be given to chain ladder when reported claims are used.
