A3. Bailey & Simon

Question 1

When to use premium base (for frequency)?

Answer 1

Premium base (for freq) only eliminates maldistribution:
1. High freq (to car-year) territories are also high avg prem territories
2. Territorial rate differentials are proper

Question 2

How to check variation of Pr(Accident) or a stable class?

+Reasons why it may not

Answer 2

The closer the credibilities (Z) for 2+, 3+ class are to 2x, 3x the credibility of 1+, the less variation and more stable

Reasons why it may not:
* Risks may be entering or leaving the class
* An individual insured’s probability of an accident changes from one year to the next

Question 3

R formula

Answer 3

R = 1 / (1-e^λ) - assumes poisson distribution
R = 1 / P(X ≥ 1) - for other distributions
λ = class total claim frequency
= total # claims / total earn car years

Question 4

Premium Formula

Answer 4

Prem = Base Rate * Exp Mod * Other Factors

Question 5

Mod & Credibility (Z)

What is it, formulas

Answer 5

Mod is relative claim frequency to total:
Mod = Freq / Freq(total)
Mod = ZR * (1-Z)

when R=0 (for 1+ years claims free):
Mod = 1-Z
Z = 1-Mod