Cas Exam 8 Bailey And Simon

Front 1

Experience Rating Formula

Back 1

Mod = ZR + (1-Z)
Z= credibility
R = Ratio of actual to expected losses

Front 2

Calculating the Mod

Back 2

(# of claims in group)/(Earned premium in group at present 0 yrs. claims-free rates) /
(# of claims in class) / (earned premium in class at present 0 yrs. claim-free rates)

Front 3

Calculating R

Back 3

Yrs Claims Free R
1+ 0
0 1/(1-exp(-lambda))

lambda = # claims from class / earned car years of insureds in class

Front 4

When to use a premium base for frequency

Back 4

Hazam states that a premium base only eliminates maldistribution if:
1. High frequency territories are also high avg. premium territories
2. Territorial rate differentials are proper

Front 5

Poisson formula

Back 5

Pr(X=k) = lambda ^ k * exp(-lambda) / (k!)

Front 6

Conclusion of paper

Back 6

1. The experience of a 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. The credibilities for varying years of experience should increase in proportion to the # of years of experience.

Front 7

Credibility for 2 and 3 years of experience relative to 1 year

Back 7

The credibility increases in proportion to the # of years only for low credibilities
The closer the credibilities for 2 and 3 years of experience are to 2 and 3 times the 1 year credibility, then the less variation in insured's probability of an accident. This could be due to:
1. Less risks entering/exiting the portfolio.
2. Risk characteristics not changing much over time.

Front 8

Buhlmann credibility

Back 8

Suppose X is a random variable with some distribution with parameter Theta, and Theta itself is a random variable with some distribution and additional parameters. In that case, the credibility of a sample of n observations from X is given by:

Z = n/(n+k)
n= # of claims in sample
k = E(Var(X|Theta)) / (Var(E(X|Theta))