credibility

Question 1

when we don’t have enough data for estimates to be stable or accurate

Answer 1

can use complement of credibility to supplement our data in attempt to improve stability and accuracy of estimate

Question 2

while losses for any one risk will vary significantly from year to year

Answer 2

average losses of large group of independent risks will be more stable due to law of large numbers

Question 3

amount of credibility given to observed experience need to meet

Answer 3

0_<Z<_1

Z should increase as n increases

Z should increase at a decreasing rate

Question 4

classical credibility

Answer 4

estimate=Z*observed+(1-Z)*related

Z=min(sqrt(n/N),1)

Question 5

6 desirable qualities for complement

Answer 5

1. accurate: close to target
2. unbiased: be on target on average
3. statistically independent from base statistic: errors can compound
4. available: otherwise not practical
5. easy to compute: otherwise difficult to justify to others
6. logical relationship to base statistic: otherwise difficult to justify to others

Question 6

Loss costs of a larger group that includes group being rated

Answer 6

• 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

Question 7

Loss costs of larger related group

Answer 7

• ex: larger neighboring state’s data
• available, easy to compute, independent, possible accurate
• usually biased
• logical relationship to subject experience is reasonable choice

Question 8

RC from larger group applied to present rates

Answer 8

C = curr LC of subject * larger group ind. LC/larger group curr avg LC

Question 9

Harwayne’s method

Answer 9

• 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

Question 10

Trended Present Rates

Answer 10

• 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

Question 11

formulas for trended present rates

Answer 11

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

Question 12

Competitor rates

Answer 12

• biased, inaccurate, difficult to obtain
• independent, easy to compute, logical relationship

Question 13

Increased limits analysis

Answer 13

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

Question 14

Lower limits analysis

Answer 14

capped data at lower limit d

C=losses capped @ d * (ILF(A+L)-ILF(A))/ILF(d)

-more bias than #1 but more accuracy

Question 15

Limits analysis

Answer 15

-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

Question 16

Fitted curves

Answer 16

-fitting curve to data -> curve can be extrapolated to higher limits with little or no data