Hurliman, Mack 2000, Clark

Question 1

Hurlimann’s method vs Benktander method

Answer 1

• Hurlimann is inspired by Benktander
• Hurlimann’s method is based on a full development triangle, where Benktander is based on a single origin period (AY/UY)
• Hurlimann’s method requires a measure of exposure for each origin period (i.e. premiums)

Question 2

Hurlimann’s two new reserving methods based on loss ratio payout factors pi

Answer 2

Individual Loss Ratio Reserve Rind (similar to Chain Ladder)
Collective Loss Ratio Reserve (Rcoll) similar to cape cod moethod

Question 3

Individual Loss Ratio Claims Reserve Formula

Answer 3

pi is the % of ult claims from origin period i expected to be paid in development period n-i+1
qi = 1-pi, % of total ult remain unpaid in development period n-i+1

Question 4

Expected loss ratio formula

Answer 4

Question 5

Collective Loss Ratio method Reserve Rcoll calculation steps

Answer 5

Question 6

Collective Loss Ratio method % reported formula pi

Answer 6

Question 7

Neuhaus loss ratio claims reserve formula

Answer 7

basically Zwn = pi * ELR

Question 8

Optimal Credibility Formula

Answer 8

Question 9

t*i formula when fi is not 1 (aka Var(Ui) not equal to Var(Ubc))

Answer 9

Question 10

Mack 2000 U0,U1,U2 definition

Answer 10

Question 11

What is Esa Hovinen assumption

Answer 11

Esa Hovinen applies the credibility mixture directly to the reserves instead of losses. When c=pk, Reh = Rgb

Question 12

Benktander (GB) Ultimate as a wtd-avg of Chain-Ladder and Expected Loss Ultimates

Answer 12

Question 13

Advantages of GB method

Answer 13

• outperform BF and CL in many circumstances
• the MSE of GB is almost as small as optimal credibility reserve

Question 14

How do Clark calculate the age to use

Answer 14

“average” accident date to evaluation date
but mostly it may be just years - 6 mo. where it’s valued by months here

Question 15

What does Growth function represent

Answer 15

G(x) = 1/CDF = % reported

Question 16

Formula for normalized residaul

Answer 16

Question 17

Parameter Variance given Covar matrix

Answer 17

Question 18

The likelihood function l that MLE is trying to maximize

Answer 18

for each cell it’s ci*ln(mui)-mui. l is just the sum over all cells

ci actual loss in AY i, development period t