Bailey & Simon

Front 1

A = ?
X = ?
Y = ?
B = ?

Back 1

A = 3 or more yrs since most recent accident or since licensing

X = 2 yrs since most recent accident

Y = 1 yr since most recent accident

B = no yrs since most recent accident or since licensing

Front 2

Why did the authors chose to calc relative claim freq on the basis of prem rather than car years?

Back 2

this avoids the maldistribution created by having higher claim freq territories produce more X, Y and B risks and also produce higher territorial prems

Front 3

experience rating formula commonly used?

Back 3

mod = ZR + (1-Z)

Z is credibility
R is ratio of actual to expected losses

Front 4

formula for how credible lack of any accidents is?

Back 4

R = 0, therefore

mod = 1 - Z, or
Z = 1 - mod

Front 5

experience rating vs. class ratemaking

Back 5

it s/b remembered that experience rating is a procedure to find the deviation of an indiv risk from the avg risk and is different from class ratemaking, which is a procedure to find the avg and where an increase in the volume of the experience increases the reliability of the indication only proportional to square root of the volume

Front 6

how is freq calculated?

Back 6

# of accidents / $1k of prem

relative freq is assumed to be the modification = (A+X freq) / tot freq

Front 7

if claims have poisson dist with mean mu,
tot expected accidents = ?
E(# of people to produce 0 accidents) = ?
implied claim freq for those risks that had at least one claim = ?

Back 7

tot expected accidents = N * mu

expected number of people to produce zero accidents = N * e^-mu

implied claim freq for those risks that had at least 1 claim = mu / (1 - e^-mu)

R reduces to 1 / (1 - e^-mu)

Front 8

conclusions

Back 8

1. the experience for 1 car for 1 yr has significant and measurable crediblity for experience rating
2. in a highly refined private passenger rating classification system which reflects inherent hazard, there wouldn't be much accuracy in an indiv risk merit rating plan, but where a wide range of hazard is encompassed w/i a classification, credibility is much larger
3. if we are given one yr's experience, and add a 2nd yr, we increase the cred roughly 2/5. Given 2 yrs experience, a 3rd yr will increase the cred by 1/6 of it's 2nd yr value

Front 9

Bailey & Simon: statement 1: in comparing credibility among classes, the cred should vary approx in proportion to avg claim freq of the class

Back 9

- assumed to be true if variation of an indiv insured's chance for an accident were the same w/i each class
- if a class is very narrowly defined (highly refined), then the likelihood is higher that any observed experience differences are truly just random, and the credibility given that experience s/b low
- so, if one class has double the freq of another class, but the cred assigned to risk free yrs substantially less than doubles, then likely explanation is that the class with double the freq is more narrowly defined

Front 10

Bailey & Simon: statement 2: w/i any class, the cred assigned to accident free experience should vary approx in proportion to # of yrs a risk has been accident free

Back 10

this is assumed to be true unless risks are entering or leaving the class, or if individual risks' true chance of a loss change from time to time w/i a yr and from one yr to the next

Front 11

Bailey & Simon: note for both statements

Back 11

the failure to hold results from a non-constant spread of actual risk potential. The difference is that if Appendix 1 fails, the spread must differ across classes; if Appendix 2 fails, the spread must differ over time w/i the same class

Front 12

Bailey & Simon: Discussion by Hazam: a prem base eliminates the maldistrubution only if:

Back 12

1. high freq territories are also high prem territories &
2. if territorial differences are proper

However, prem, although not perfect, is an improvement over exposure as a base for this type of study

Front 13

Bailey & Simon: Discussion by Hazam: his comment on appendix statements

Back 13

from paper: "the credibilities for experience periods of 1, 2, and 3 yrs would be expected to vary approx in proportion to 3 of yrs"

this holds largely true only for low credibilities; large credibilities would render such a statement inaccurate