Bailey & Simon - cred for single yr

Question 1

Bailey & Simon demonstrate

Answer 1

that a single car’s experience for a single year has significant and measurable credibility for experience rating

-also show that credibility of individual risk experience within a class varies based on how narrowly the class is defined

Question 2

B&S ask

Answer 2

what does merit rating plan data imply about credibility of experience from a single car for 1 year

Question 3

experience rating credibility depends

Answer 3

not just on volume of data but also variance of loss experience within a class

Question 4

B&S come to 3 conclusions

Answer 4

1. experience of single car for 1 year has significant and measurable credibility for experience rating
2. individual risk experience is more credible when there is more variance in loss experience within a risk class, which occurs in less refined risk classification systems
3. credibilities for varying years of experience should increase in proportion to # of years of experience (if chance of accidents for individual risks remains constant and no risks enter or leave class)

Question 5

simple Buhlmann credibility example is shown to demonstrate that double or triple the data (double or triple the experience) doesn’t

Answer 5

doesn’t result in exactly double or triple the credibility

Question 6

2 reasons why credibility wouldn’t increase in proportion to # of yrs ?

Answer 6

Risks entering/exiting portfolio

Risk characteristics changing over time

Question 7

the greater difference between individual risks in a class

Answer 7

more powerful individual risk rating will become

Question 8

if variance in loss experience between risks is largely explained by classification rating variables, then

Answer 8

experience rating wouldnt add much predictive power

Question 9

what exposure base is used in study?

Answer 9

didnt define frequency as claim count/exposure

used EP @ current class B rates as base for frequency

*to avoid maldistribtion

*possible exposure correlation between territory rating variable and merit rating variable

ie higher frequency territories produce more X, Y, and B risks and higher premiums

Question 10

premium base for frequency only eliminates maldistribution if

Answer 10

1. high frequency to car-year territories are also high average premium territories
2. territorial rate differentials are proper; one sign of this would be equal LRs across territories

Question 11

credibility for individual risk is lowered when

Answer 11

class plan is highly refined because it is more difficuly to identify differences in loss potential for particular risk at hand from average risk in class

Question 12

Derive R for drivers with one or more claims in the past year.

Answer 12

risks accident free=N*e^(-λ)

Pr(accident free)=e^(-λ)

Pr(at least 1 accident)=1-e^(-λ)

avg # claims last year=Nλ

frequency=Nλ/N*(1-e^(-λ))=λ/(1-e^(-λ))

past relative claim frequency = R = [λ/(1-e^(-λ))]/λ = 1/(1-e^(-λ))

Question 13

testing for maldistribution

Answer 13

look at frequency (claims/car yrs), avg premium (prem/car yrs), and LR by territory

if LRs are the same, then suggests territory relativities are proper

if higher frequency territories do not have higher average premiums then it is advisable to use earned car years instead of EP for exposure base

Question 14

2 assumptions in selecting EP as exposure base

Answer 14

hgih freq territories are also high average prem territories

territorial differentials are proper