Hurlimann Flashcards
Key differences b/w Hurlimann and Benktander methods (2)
- Hurlimann’s method uses multiple origin periods (entire triangle) vs. a single origin period
- requires a measure of exposure (prem) in each origin period
Formula for incremental and overall loss ratios (m_k’s)
m-sub k = sum of incremental losses in column k / premiums for corresponding origin periods
sum of m-ks = overall LR
Expected value of the burning cost formula
= premium for origin period * overall LR
Loss ratio payout factor interpretation and formula
% emerged to date
p-sub i = sum of m-sub k’s to date / overall LR
What makes the collective loss ratio claims reserve different from the BF method?
uses burning cost estimate (collective claims experience, data) instead of a priori estimate
Advantage of the collective loss ratio reserve over the BF reserve
different actuaries always come to the same results provided they use the same premiums (opposite of Mack result)
Neuhaus credibility weight
Z = p_i x LR to date
= % emerged * overall LR
Optimal credibility weight (Z*) which minimizes the MSE of reserves
Zi* = p_k / (p_k + sqrt(p_k))
Assumption that simplifies ti = sqrt (% emerged) for optimal credibility weight
Var(ultimate claims) = Var(BC ultimate)
Formula for MSE of reserves
Hurlimann
MSE(Rc,i) = E(a^2(U_i) * [Z_i^2/p_i + 1/q_i + (1-Z_i)^2/t_i] * q_i^2
where t_i will likely be given or will be sqrt(p_i)
Z = 1 gives mse(R_ind) = E(a^2(U_i) * q_i/p_i
Z = 0 gives mse(R_coll) = E(a^2(U_i) * q_i * (1 + q_i/t_i)
Cape Cod credibility method
R-ind = q / p * V (V = premium) R-coll = q * LR * V LR = sum latest cumulative losses / sum used-up premium Zi = % emerged = p_i
w/% emerged calculated from CL LDFs
Optimal Cape Cod and optimal BF method credibility
Zi = p / (p + sqrt(p)
p = % emerged
w/% emerged calculated from CL LDFs
