Mack (2000)

Question 1

Û (relationship between Û and R^

Answer 1

Û =C_k+R^

Question 2

p_k

Answer 2

the proportion of the ultimate claims amount which is expected to be paid after k years of development

Question 3

q_k

Answer 3

1-p_k

The proprotion of the ultimate claims amount which is expected to remain unpaid after k years of development

Question 4

R_BF

Answer 4

reserve estimate based on the a priori expectation of ultimate losses:

R_BF= q_kU₀

Assumes current claim count C_k is not predictive of future claims

Question 5

U_BF

Answer 5

U_BF=C_k + R_BF

Question 6

U_CL

Answer 6

U_CL = C_k/p_k

Question 7

R_CL

Answer 7

R_CL = U_CL - C_k

R_CL = q_kU_CL

Assumes current claims amount is fully predictive of future claims

Question 8

Advantage of CL over BF

Answer 8

Using CL, different actuaries obtain similar results. This is not the case with BF due to differences in the selection of U₀

Question 9

U_c (Benktander a priori Ultimate)

Answer 9

U_C = cU_CL + (1-c)U₀

credibiltiy mixture of U₀ and CL Ultimate

Question 10

R_GB

Answer 10

assume c = p_k

R_GB = q_kU_BF

Question 11

U_GB

Answer 11

U_GB = C_k + R_GB = (1-q_k)U_CL + q_kU_BF

credibility weighted average of the BF method and CL method, where c = p_k

Question 12

Esa Hovinen Reserve (R_EH)

Answer 12

R_EH = cRCL + (1-c)R_BF

_IIf we set c = p_k, R_EH = R_GB

Question 13

4 Reasons Benktander Method is superior to BF and CL

Answer 13

1. Lower Mean Squared Error
2. Better approximation of the exact Bayesian procedure
3. Superior to CL since 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