Hurlimann

Question 1

Key differences b/w Hurlimann and Benktander methods (2)

Answer 1

1. Hurlimann’s method uses multiple origin periods (entire triangle) vs. a single origin period
2. requires a measure of exposure (prem) in each origin period

Question 2

Formula for incremental and overall loss ratios (m-sub k’s)

Answer 2

m-sub k = sum of incremental losses in column k / premiums for corresponding origin periods

sum of m-ks = overall LR

Question 3

Expected value of the burning cost formula

Answer 3

= premium for origin period * overall LR

Question 4

Loss ratio payout factor interpretation and formula

Answer 4

% emerged to date

p-sub i = sum of m-sub k’s to date / overall LR

Question 5

What makes the collective loss ratio claims reserve different from the BF method?

Answer 5

uses burning cost estimate (collective claims experience, data) instead of a priori estimate

Question 6

Advantage of the collective loss ratio reserve over the BF reserve

Answer 6

different actuaries always come to the same results provided they use the same premiums (opposite of Mack result)

Question 7

Neuhaus credibility weight

Answer 7

Z = cumulative LR to date

= % emerged * overall LR

Question 8

Optimal credibility weight (Z*) which minimizes the MSE of reserves

Answer 8

Zi* = % emerged / (% emerged + ti)

where ti = (fi - 1 + sqrt((fi + 1) * (fi - 1 + 2pi)) ) / 2

Question 9

Assumption that simplifies ti = sqrt (% emerged) for optimal credibility weight

Answer 9

Var(ultimate claims) = Var(BC ultimate)

Question 10

Formula for MSE of reserves

Hurlimann

Answer 10

MSE(Ri) = E[alpha^2(Ui)] * [ Zi^2 / % emerged + 1 / (1 - % emerged) + (1 - Zi)^2 / ti ] * (1 - % emerged)^2

Question 11

Cape Cod credibility method

Answer 11

R-ind = (1 - % emerged) / % emerged * latest claims 
R-coll = (1 - % emerged) * LR * premium
LR = sum latest cumulative losses / sum used-up premium
Zi = % emerged 

w/% emerged calculated from CL LDFs

Question 12

Optimal Cape Cod and optimal BF method credibility

Answer 12

Zi = % emerged / (% emerged + sqrt( % emerged)

w/% emerged calculated from CL LDFs

Question 13

Formula for t(I)

Hurlimann

Answer 13

t(I) = (f(I) - 1 + sqrt((f(I) + 1) * (f(I) - 1 + 2p(I))) / 2

Var(U(I)) = f(I) * Var(U(I)-BC)