Mack (2000) - Benktander

Question 1

what is the BF RESERVE estimate based on?

Mack 2000

Answer 1

a priori expectation of ultimate losses

Question 2

what does BF method assume?

Mack 2000

Answer 2

it assumes the current claims amount (C_k) is not predictive of future claims (because it uses U_0)

Question 3

what does the CL method assume?

Mack 2000

Answer 3

assumes current claims amount C_k is fully predictive of future claims (because it uses U_CL)

Question 4

what is an advantage of CL over BF?

Mack 2000

Answer 4

different actuaries obtain similar results (vs. BF, results depend on selection of U_0)

Question 5

what is the relationship between C_k and credibility?

Mack 2000

Answer 5

as claims (C_k) develop, credibility should increase

Question 6

why is GB also called the “Iterated BF”?

Mack 2000

Answer 6

it’s obtained by applying the BF procedure twice, first to U_0, then to U_BG

Question 7

what happens if we iterate through the credibility-weighting process indefinitely?

(Mack 2000)

Answer 7

we eventually end up with the CL result

Question 8

what are 4 reasons the Benktander method is superior to BF and CL?

(Mack 2000)

Answer 8

1. Lower MSE
2. Better approximation of the exact Bayesian procedure
3. Superior to CL because it gives more weight to the a priori expectation of ultimate losses
4. Superior to BF since it gives more weight to actual loss experience.

Question 9

when is MSE ( R_GB) < MSE (R_BF) ?

Mack 2000

Answer 9

when c* (optimal credibility reserve that minimizes MSE) > p_k / 2
(implies that c* is closer to c = p_k than c = 0)
Benktander MSE is almost always smaller than BG & CL