C.5 Credibility

Question 1

3 necessary criteria for credibility

Answer 1

1. 0= 0
2. Z should increase as n increases at a decreasing rate.
   Mathematically: d/dn (Z/n) < 0

Question 2

Formulas for Classical and Bühlmann credibility

Answer 2

Classical: Z = min(sqrt(n/N0), 1)

Bühlmann: Z = N/(N+K)

Question 3

6 desirable qualities for a complement of credibility

Answer 3

1. Accurate: i.e., should be close to the target
2. Unbiased: i.e., should be on target on average
3. Statistically independent from the base statistic:
   otherwise errors can compound
4. Available: otherwise not practical
5. Easy to compute: otherwise difficult to justify to others
6. Logical relationship to base statistic: otherwise difficult to justify to others

Question 4

Advantages and disadvantages of complement: Loss
costs of a larger group that includes the group being
rated

Answer 4

The advantages of this approach are accuracy (more data leads to more stability), availability, and being easy to compute. If a reasonable choice is made, it can also
have a logical connection to the subject experience. If the subject experience is excluded from the complement, then the complement may also be independent. The disadvantage of this approach is that it can be biased, since there is a reason the subject group has been separated from the larger group.

Question 5

Advantages and disadvantages of complement: Loss

costs of a larger related group

Answer 5

This complement is usually biased, but it is generally
available, easy to compute, independent from the subject experience, and possibly accurate. It may have a logical relationship to the subject experience if chosen reasonably.

Question 6

Advantages and disadvantages of complement: Rate

change from the larger group applied to present rates

Answer 6

This complement is usually unbiased, but it is generally
available, easy to compute, independent from the subject experience, and possibly accurate. It may have a logical relationship to the subject experience if chosen reasonably.

Question 7

Advantages and disadvantages of complement:

Harwayne’s Method

Answer 7

This complement is unbiased, accurate, mostly independent, available, and has a logical relationship to the subject experience. Since it is a little harder to compute, it is also harder to explain the logical relationship to the subject experience.

Question 8

Advantages and disadvantages of complement:

Trended Present Rates

Answer 8

This complement may or may not be accurate based on
stability of indications, it is unbiased, it may or may not be
independent, it is readily available, it is easy to compute, and it has a logical relationship to the subject experience.

Question 9

Trended Present Rates pure premium and loss ratio

formulas

Answer 9

When using the pure premium method, the complement is:
C = Current Rate x Loss Trend Factor x
(Prior Indicated Loss Cost/ Loss Cost Implemented with Last Review)

When using the loss ratio method, the complement is:
C = (Loss Trend Factor/ Premium Trend Factor Prior) x (Indicated Rate Change Factor/Prior Implemented Rate Change Factor)

The first fraction above is called the Loss Ratio Trend Factor.

Question 10

Advantages and disadvantages of complement:

Competitor’s rates

Answer 10

This can be biased, inaccurate, and difficult to obtain.

However it is independent, easy to compute, and has a logical relationship to the subject experience.

Question 11

Increased Limits Analysis Complement formula and

advantages/disadvantages

Answer 11

The complement for the layer L excess of A is:

C = Losses capped at A x (ILF(A+L) -

Question 12

Lower Limits Analysis Complement formula and

advantages/disadvantages

Answer 12

The complement for the layer L excess of A is:

C = Losses capped at d x (ILF(A+L) -

Question 13

Limits Analysis Complement formula and

advantages/disadvantages

Answer 13

The complement for the layer L excess of A is:
C = Expected Loss Ratio x Sum (d>A) of
Premium(d) x (ILF(min(d,A+L)) -

Question 14

Fitted Curves Complement formula and

advantages/disadvantages

Answer 14

(Skipped integral formula)

If the fitted curve is accurate, then this approach is more
accurate, less biased, has a logical relationship to the subject experience, and is more stable than the other methods. However, it is less independent since the underlying data is needed to fit the curve. Also, it is not easy to compute, and the data may not be available.