Mack (2000) Flashcards
notations: pk, qk, Ck
pk = % Paid = 1/CDF
qk = % Unpaid = 1-1/CDF
Ck = cumulative paid losses
relationship btwn pk, qk and CDF
pk = 1/CDF => CDF = 1/pk
qk = 1-1/CDF => CDF = 1/(1-qk)
Method 1 - Benktander method as a second iteration of the BF procedure
Method 2 - Benktander method as a credibility-weighting of the Chain Ladder and
Expected Loss Ultimates
Method 3 - Benktander reserve as a credit-weighting of CL and BF reserves
Esa Hovinen Reserve
R(EH) = c R(CL) + (1-c) R(BF)
If c = pk, R(EH) = R(GB)
Iterated BF Method - formulae only
Iterated BF Method - formulae + visual
Advantages of the Benktander Method
- Outperforms the BF and Chain Ladder methods in many circumstances
- The MSE of the Benktander reserve is almost as small as that of the optimal credibility reserve
- Better approximation of the exact Bayesian procedure
- Superior to CL since it gives more weight to the a priori expectation of ultimate losses
- Superior to BF since it gives more weight to actual loss experience
If c*___ => Benktander reserve has smaller MSE
c* > pk/2
Briefly describe when the Benktander ultimate loss estimate would be greater than the Bornhuetter-Ferguson ultimate loss estimate as of December 31, 2018.
Since the Benktander estimate is a weighting of the CL estimate and BF estimate
=> Benktander estimate is greater than the BF estimate when the CL estimate is greater than the BF estimate
Explain why it may not be appropriate to use the Bornhuetter-Ferguson method when losses develop downward.
Since the BF IBNR does not respond to actual loss performance
=> the downward development will not affect IBNR produced by the BF method
If the downward development represents real trends (such as increased sal/sub)
=> the BF method will overstate the IBNR
