credibility Flashcards
when we don’t have enough data for estimates to be stable or accurate
can use complement of credibility to supplement our data in attempt to improve stability and accuracy of estimate
while losses for any one risk will vary significantly from year to year
average losses of large group of independent risks will be more stable due to law of large numbers
amount of credibility given to observed experience need to meet
0_<Z<_1
Z should increase as n increases
Z should increase at a decreasing rate
classical credibility
estimate=Z*observed+(1-Z)*related
Z=min(sqrt(n/N),1)
6 desirable qualities for complement
- accurate: close to target
- unbiased: be on target on average
- statistically independent from base statistic: errors can compound
- available: otherwise not practical
- easy to compute: otherwise difficult to justify to others
- logical relationship to base statistic: otherwise difficult to justify to others
Loss costs of a larger group that includes group being rated
- ex: regional or CW data as complement to state data, multiple years of data as complement to single year of data
- complement can include or exclude subject experience
- accuracy, availability, being easy to computer
- logical relationship to subject experience is reasonable choice
- complement may be independent if subject is excluded
- can be biased since there is reason subject group has been separated from larger group
Loss costs of larger related group
- ex: larger neighboring state’s data
- available, easy to compute, independent, possible accurate
- usually biased
- logical relationship to subject experience is reasonable choice
RC from larger group applied to present rates
C = curr LC of subject * larger group ind. LC/larger group curr avg LC
Harwayne’s method
- adjusts overall LC differences between states and exposure distributional differences between states to calc C
- example for complement for class 1 in state A
PP for A
PP for B and C using A’s exposures: PP’(B)
Adj factors for state B and C =PP(A)/PP’(B)
State B, Class 1 adjusted = Adj factor*PP(1,B)
C=sum(exposures(1,i)*state i class 1 adjusted)/sum(exposures(1,i))
- unbiased, accurate, mostly ind, logical relationship
- harder to compute so harder to explain logical relationship
Trended Present Rates
- used when no larger group for use as complement
- complement is current rates with 2 adjustments
- adjust to latest indicated rates in case full indication was not taken after last review
- adjust for any trend since last rate review
- trend from = original target effective date from last rate review
- trend to = target effective date of next rate change
- complement may or may not be accurate based on stability of indications, may it may not be independent
- unbiased, readily available, easy to compute, logical relationship
formulas for trended present rates
PP: C=Curr rate*loss trendfactor* prior Ind LC/LC implemented at last review
LR: C=LR trendfactor*prior Ind RCF/RCF implemented at last review
Competitor rates
- biased, inaccurate, difficult to obtain
- independent, easy to compute, logical relationship
Increased limits analysis
when ground-up loss data up to attachment point is available
-complement for layer L excess of A
C=Loss capped @ A*(ILF(A+L)-ILF(A))/ILF(A)
- if ILFs are based on different size of loss dist than subject experience, then biased
- independent and practical if data is available
- relationship to subject may not be logical due to possible bias
- may be inaccurate due to low volume of data
Lower limits analysis
capped data at lower limit d
C=losses capped @ d * (ILF(A+L)-ILF(A))/ILF(d)
-more bias than #1 but more accuracy
Limits analysis
-further generalization of #1 but now use data capped at all limits greater than attachment point A
C=ELR*sum(Prem(d)* (ILF(min(d,A+L))-ILF(A))/ILF(d))
- biased and inaccurate
- assumes ELR does not vary by limit
