Hurlimann Flashcards
Calculate the collective reserve estimate
R=q(VxELR) V=premium or other exposure base Similar to BF method
Calculate % reported
m=sum of losses in column/sum of corresponding premium pi=mi/sum(m)
Credibility options for individual and collective methods
Z=1 Chain ladder Z=0 BF Z=p Benktander Z=pxELR Neuhaus Z=p/(p+sqrt(p)) Optimal R=ZxR(ind)+(1-Z)R(coll)
Calculate the individual reserve estimate
R=qC/p q=% unreported p=%reported C=paid to date Equivalent to chain ladder
Full credibility formula
Briefly describe three differences between Hurlimann’s method and the Benktander method.
- Hurlimann’s method is based on a full development triangle, whereas the Benktander method is based on a single accident year
- Hurlimann’s method requires a measure of exposure for each accident year (i.e. premiums)
- Hurlimann’s method relies on loss ratios (rather than link ratios) to determine reserves
Briefly describe one similarity between Hurlimann’s method and the Benktander method.
Similar to the Benktander method, H¨urlimann’s method represents a credibility weighting between two extreme positions: relies on cumulative paid claims (i.e. individual loss reserves) vs. ignores cumulative paid claims (i.e. collective loss reserves)
Provide one advantage of the collective loss ratio reserve over the standard Bornhuetter/Ferguson reserve.
Similar to the Benktander method, H¨urlimann’s method represents a credibility weighting
between two extreme positions: relies on cumulative paid claims (i.e. individual loss
reserves) vs. ignores cumulative paid claims (i.e. collective loss reserves)
Explain why t=sqrt(p) is an appealing choice when calculating the optimal credibility weights.
This assumption yields the smallest credibility weights for the individual loss reserves, which places more emphasis on the collective loss reserves
