G.3 Bornhuetter-Ferguson Method Flashcards
Bornhuetter-Ferguson Formula for Estimated
Ultimate Claims using reported claims data
B-F Ultimate = Actual Reported + Expected Unreported
Claims
B-F Ultimate = Actual Reported + Expected Claims x %
Unreported
B-F Ultimate = Actual Reported + Earned Premium
Expected Claim Ratio x % Unreported
Bornhuetter-Ferguson Formula for Estimated
Ultimate Claims using paid claims data
B-F Ultimate = Actual Paid + Expected Unpaid Claims
B-F Ultimate = Actual Paid + Expected Claims x % Unpaid
B-F Ultimate = Actual Paid + Earned Premium Expected
Claim Ratio x % Unpaid
How the B-F method is a credibility weighting of
other methods
B-F Ultimate = Development Technique Ultimate x (1/CDF)
+ Expected Claims x (1 - 1/CDF)
This is essentially a credibility-weighting with credibility Z = (1/CDF).
Benktander Formula for Estimated Ultimate Claims
using reported claims data
Benktander Ultimate Claims = Actual Reported Claims + B-F Ultimate x % Unreported
How the Benktander method is a credibility
weighting of other methods
Benktander Ultimate = Development Technique Ultimate x (1/CDF) + B-F Ultimate x (1 - 1/CDF)
This is essentially a credibility-weighting with credibility Z = (1/CDF).
What happens with many iterations of the
Benktander method?
More and more weight is given to the Development technique with each iteration, so the Benktander estimates approach the Development technique estimates.
Assumptions of B-F Method
The main assumption is that IBNR or unpaid claims for an
exposure period can be better estimated based on an a priori estimate than using the experience observed to date for that exposure period. Another way of stating this is that the claims reported and paid to date for that exposure period tell you no useful information about your IBNR or unpaid claims for that exposure period.
A secondary assumption is that a reasonable expected claim ratio can be obtained.
Common uses of the B-F Method
-When there are random fluctuations or large claims at early maturities.
-When entering a new line of business.
-When estimating ultimates at early maturities for
long-tailed lines of business where the early age-to-ultimate factors are highly leveraged.
Advantages of the B-F and Benktander Methods
The B-F method has the advantages of providing more
stable estimates than the Development technique and more responsive estimates than the Expected Claims technique.
The Benktander method has the advantage of being even more responsive than the B-F method while still being more stable than the Development technique (but not as stable as B-F).
2 challenges of using the B-F and Benktander Methods
- Estimating the expected claims.
2. Estimating the expected % unreported (or % unpaid).
When the credibility interpretation of the B-F and
Benktander methods does not hold
When there is downward development, because the
“credibility” that is equal to 1/CDF will be greater than 1.
Options for dealing with downward development in
using the B–F or Benktander method
-Continuing to use the B-F and Benktander methods.
-Limiting the CDFs to a minimum value of 1.
-Rely on a different technique to select ultimates for years with CDFs below 1.
How speedups or slowdowns in settlement impact
the B-F and Benktander methods
When dealing with the reported B-F or Benktander methods, estimates will still be accurate since both the Development and Expected Claims estimates based on reported claims will be accurate.
The paid B-F or Benktander methods will overestimate
when there has been a speedup in settlement, and
will underestimate when there has been a slowdown in
settlement. However, the error will not be as big in magnitude as it would be using the Development technique, since the weight given to the Expected Claims technique reduces the amount of the error.
How changes in case reserve adequacy impact the B-F
and Benktander methods
When dealing with the paid B-F or Benktander methods,
estimates will still be accurate since both the Development and Expected Claims estimates based on paid claims will be accurate.
The reported B-F or Benktander methods will overestimate when there has been an increase in case reserve adequacy, and will underestimate when there has been a decrease in case reserve adequacy. However, the error will not be as big in magnitude as it would be using the Development technique, since the weight given to the Expected Claims technique reduces the amount of the error.
How changes in claim ratios impact the B-F and
Benktander methods
The B-F and Benktander techniques do not fully react to
changes in claim ratios due to the weighting given to the
Expected Claims technique. Note that reported B-F and
Benktander methods will be more responsive than paid B-F and Benktander methods since more weight will be given to the Development technique when reported claims are used.
