Bailey & Simon

Question 1

Describe how to chose between premium or exposure base

Answer 1

Using premium ensures higher freq territories are not doubly penalized for having high freq and more non-A risks

If no territories, both will give identical mod

Maldistribution is only corrected if:
1. High freq territories also have high premiums
2. Territorial differentials are proper (equal LRs)

Question 2

Explain Bailey & Simon approach to experience rating

Answer 2

Usually, we calculate Mod = ZR + (1-Z) from historical and established credibility

B&S look at this backward:
Use current policy term data to figure ideal Mod
Estimate R for prior term
Plug Mod and R to solve for Z = (Mod - 1) / (R-1)

Question 3

How do we calculate R

Answer 3

Ratio of relative frequency to premium from last year’s experience

If you do not have data, we can approx R for B rating:
1. Poisson R = 1/(1 - exp(-lambda))
2. NB R = 1/(1 - (1 - lambda/(r + lambda))^r)

Question 4

Why is individual risk experience more credible when more variance in loss experience within risk class

Answer 4

Experience rating credibility depends not just on volume of data but also on variance of loss experience within class

When classes are more narrowly defined, risks within those classes are more similar to each other.

Since experience rating distinguishes the individual risk from class average risk, it has less credibility.

Question 5

How ratios of credibility for 2 and 3 years of claim-free to 1y can be used to compare stability between books of business

Answer 5

The closer Z2+/Z1+ is to 2 and Z3+/Z1+ is to 3, the less variation in an insured’s prob of accident for that class (ie risks in group are not changing over time)

If lower values, could be due to risks entering/exiting portfolio or risk characteristic changing over time

Question 6

Explain the 3 conclusions of B&S paper

Answer 6

1. Experience of a single car for 1y has significant and measurable credibility for experience rating
2. Individual risk experience is more credible when more variance in loss experience within risk class which occurs in less refined risk classification systems
3. Credibility for varying years of experience should increase in proportion to number of years
   This only holds if credibilities are low, risks are not entering/exiting and risk characteristics are not changing over time

Question 7

How do you calculate Mod(2+)

Answer 7

Mod(2+) = ((Tot claims for 2+ groups)/(Exposure for 2+ groups))/((Tot claims)/(Tot exposures)) = Frequency for 2+ / Tot Frequency