Hurlimann Flashcards
what are two differences between Hurlimann’s method and the Benktander method?
(Hurlimann)
- Hurlimann is based on a full development triangle (vs. Benktander is based on a single origin period - AY, UW Yr)
- Hurlimann requires a measure of exposure for each origin period (i.e. premiums)
what are 3 standard reserving methods that rely on link ratios to determine reserves?
(Hurlimann)
- chain-ladder
- Bornhuetter/Ferguson
- Cape Cod
what does Hurlimann’s method rely on instead of link ratios?
Hurlimann
loss ratios
what is the main result of Hurlimann’s method?
Hurlimann
provides an optimal credibility weight for combining the chain-ladder aka individual loss ratio reserve with the BF aka collective loss ratio reserve
what is the individual loss ratio reserve?
Hurlimann
a.k.a chain-ladder
grossed-up latest claims experience of an origin period
what is the collective loss ratio reserve?
Hurlimann
experience-based burning cost estimate of the total ultimate claims of an origin period
why is the “individual” total ultimate claims considered “individual”?
(Hurlimann)
depends on the individual latest claims experience of an origin period
why is the “collective” loss ratio claims reserve considered “collective”?
(Hurlimann)
depends on the portfolio claims experience of all origin periods
what is an advantage of the collective loss ratio claims reserve over the BF reserve?
(Hurlimann)
different actuaries always come to the same results (provided they use the same premiums)
what extreme position does the individual claims reserve represent?
(Hurlimann)
assumes the cumulative paid claims amount C_i, n-i+1 is fully credible for future claims and ignores the burning cost U_i^BC of the total ultimate claims
what extreme position does the collective claims reserve represent?
(Hurlimann)
ignores the cumulative paid claims and relies fully on the burning cost (a priori estimate)
what is the credible loss ratio claims reserve?
Hurlimann
mixture of the individual and collective loss ratio reserves
what happens if we iterate between reserves and ultimates indefinitely?
(Hurlimann)
we eventually end up with the individual loss ratio estimate for ultimate claims
what is appealing about the special case where Var(U_i) = Var(U_i^BC)?
(Hurlimann)
it yields the smallest credibility weights for the individual loss reserves, which puts more emphasis on collective loss reserves
what is Z_i equal to for the collective loss ratio?
Hurlimann
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