Hurlimann

Question 1

Table structure for Hurlimann Benktander

Answer 1

AY | Prem | %paid | %unpaid | Cum Loss | Rind | Rcoll | Zi | Benktander Reserve

Question 2

Expected Incremental LR (mk) formula

Answer 2

Sum of Inc Loss / Sum prem for each incremental triangle column k

Question 3

ELR

Answer 3

Sum of mk

Question 4

% paid

Answer 4

Sum of dev periods to date mk / ELR

Question 5

R ind - CL equivalent

Answer 5

%unpaid * Cumulative Loss / %paid

Question 6

R coll - BF equivalent

Answer 6

%unpaid * Prem * ELR

Question 7

Benktander Zi

Answer 7

%paid

Question 8

Neuhaus Zi

Answer 8

%paid * ELR

Question 9

Optimal Zi when Var(U) = Var(BC)

Answer 9

%paid / (%paid + sqrt(%paid))

Question 10

Benktander Reserve

Answer 10

Zi * Rind + (1-Zi) * Rcoll

Question 11

Optimal Cred when Var(U) differs from Var(BC)

Answer 11

f = Var(U) / Var(BC)
t_opt = (f - 1 + sqrt((f + 1)*(f -1 + 2p))) / 2

Zopt = p / (p + t_opt)

Question 12

What does optimal credibility weight minimize?

Answer 12

The variance of credible loss reserves and MSE

Question 13

Advantages of Hurlimann over Mack

Answer 13

Mack requires an ELR assumption so different actuaries might come up with different reserve estimates; Rcoll does not rely on an a priori value