Estimation of Policy Liabilities

Question 1

Benktander Ultimate as 2nd Iteration of BF Procedure

Answer 1

U_GB = C + q*U_BF

Question 2

Benktander Ultimate as Weighting of CL and Expected Ultimate Loss

Answer 2

U_GB = (1 - q^2)U_CL + (q^2)U_0

Question 3

Benktander Reserves as Weighting of CL and BF Reserves

Answer 3

R_GB = (1 - q)R_CL + qR_BF

Question 4

Advantage of Benktander Method over CL and BF

Answer 4

Benktander outperforms CL and BF in many situations, with MSE close to optimal credibility reserve.

Question 5

Advantage of CL over BF and Benktander

Answer 5

With BF and Benktander, different actuaries may arrive at different results because of subjectivity in selecting U_0.

Question 6

Individual Loss Ratio Reserve Estimate

Answer 6

R_ind = q*C/p
U_ind = C/p

Question 7

Collective Loss Ratio Reserve Estimate

Answer 7

R_coll = q*EP*ELR
U_coll = C + q*EP*ELR

Question 8

Credibility-Weighted Loss Ratio Reserve Estimate

Answer 8

R = ZR_ind + (1 - Z)R_coll

Question 9

Credibility Weight for Benktander Reserves

Answer 9

Z_GB = p

Question 10

Credibility Weight for Neuhaus Reserves

Answer 10

Z_WN = P*ELR

Question 11

Credibility Weight for Optimal Reserve Estimate

Answer 11

Z_opt = p / (p + sqrt(p)) if Var(U) = Var(U_BC)

Question 12

Optimal Credibility Weight

Answer 12

f = Var(U) / Var(U_BC)
t = (f - 1 + sqrt((f + 1)*(f - 1 + 2p))) / 2
Z_opt = p / (p + t)

Question 13

Burning Cost of Total Ultimate Claims

Answer 13

U_BC = ELR*EP

Question 14

Advantage of Collective Loss Ratio Reserve over Traditional BF

Answer 14

Different actuaries come to the same result if the same premiums are used, because judgment isn’t used to select the ELR.

Question 15

MSE for Credibility-Weighted Loss Ratio Reserve Estimate

Answer 15

MSE = E[alpha^2(U)](Z^2/p + 1/q + (1 - Z)^2/t)q