B2. Experience Rating

Question 1

Advantage of experience rating

Answer 1

1. Accounts for differences between risks in a class
2. Accounts for variables that are difficult to quantify
3. Further refinement of classification beyond manual rates

Question 2

Goals of experience rating

Answer 2

1. Greater risk equity ( the degree of the charge based on the past experience should be the degree of which it is predictive of future losses)
2. Safety incentive (by charging insureds a higher premium for prior losses, insureds have a financial incentive for loss control)
3. Enhance market competition (helps guarantee equal profit potential, more companies are willing to sell)

Question 3

3 conditions for credibility Z

Answer 3

1. 0<=Z<=1
2. d/dE(Z) >=0, credibility does not decrease as size of risk increases
3. d/dE(Z/E) <=0 , % of change for any loss decreases as size of risk increases

Question 4

Buhlmann credibility

Answer 4

Z = E/(E+K)
K = EPV?VHM

Question 5

No split plan emod

Answer 5

1+ Z* (A-E)/E

Question 6

Single Split plan emod

Answer 6

1+ Zp(Ap-Ep)/E + Ze(Ae-Ee)/E
loss-free mod =[ (1-Zp)Ep + (1-Ze) Ee ] /E
Primary amount reflects claim frequency, excess amount reflects severity
Works better when parameter risks and process risks can be separated

Question 7

Quintile Test for testing the experience rating

Answer 7

1. Sort risks by emod in increasing order
2. Group the sorted risks into quintiles
3. For each quintile, calculate the manual LR and standard LR using weighted average
   If premium is not available, use actual loss/expected loss for manual, and actual loss/modified expected loss for standard.
4. Under a plan performing ideally:
   - Maximum dispersion in manual LRs (identifying risk differences)
   - Flat standard LRs across each quintiles, less dispersion means more equitable (plan corrects for risk differences, an appropriate credibility has been given to the actual loss experience)

Question 8

Efficiency test for testing experience rating

Answer 8

Test statistics = var(standard LR)/ var(manual LR)
lower test statistics indicate better performance