A3. An actuarial note on the credibility of experience of a single private passenger car

Question 1

Reasons to use a premium base for frequency

Answer 1

-higher frequency territories have higher avg premium due to territory differentials of class rating
-however, higher frequency territories also
produce more X, Y and B risks => this would increase the avg premium due to experience rating
-therefore using a premium base for frequency cancels the territory differentials and avoid the maldistribution/overlap between class rating and experience rating

**is use car-years as the denominator of frequency, the credibility calculation would account for both “within territory differences” and “between territory differences”. However, territory relativities already account for the between territory differences. Compounding territory relativities with credibility would doublecount the between territory differences, and therefore the credibility would be overstated.
Therefore, claims free drivers would be undercharged while other drivers would be overcharged.

Question 2

Conditions to use a premium base for frequency

Answer 2

Conditions:

1. high frequency territories are also high average premium territories (prm/units) ‘’ there is correlation between territories and number of yrears free claims ‘’ Frequency varies by territory
2. territorial differentials are properly reflected in rating => loss ratios are constant between territories

**if data is split by other variables, need to aggregate by territory before testing the 2 conditions

Question 3

Conclusions of paper

Answer 3

1. The experience of 1 insured for 1 year has significant and measurable credibility:
   - can be used to segment risks within a class
2. The credibility depends on the variance in individual hazards within the class ( merit rating) , not only the volume of data ( class rating):
   - if refined classification plan => already reflects inherent hazard => not much credibility in individual merit rating plan
   - Z is higher when there is more variance within a class
3. If the credibility does not increase linearly in proportion to the # of years of experience:
   - the class of insureds is not stable ( -risks entering and leaving the class)
   - the chance of accident for and inidividual insured varies over time ( risks characteristics in a group are changing over time )
   - the risk distribution is skewed

Question 4

if variance in loss experience between risks is largely explained by classification rating variables, then

Answer 4

experience rating wouldnt add much predictive power

Experience rating distinguishes the individual risk from the class average risk. So individual risk experience is more credible when there is more variance in loss experience

in homogeneous class , do no want to assign a lot of credbility to an individual since their experiencce is most similar to other risks in class

Question 5

Premium adjustements for relative frequency calculation

Answer 5

• Premium shoud be on level so we didnt double count the impact of past rate change when calculating the experience mod
• Premium should have the current merit rating factors backed out , since we will be replacing * the merit rating factors with the experience mod*

Question 6

Bailey and Simon assumptions for calculating R

Answer 6

1. Class total claim frequency to Earned car years is the same each year ***
2. Claim counts are Poisson distributed

Question 7

Hazam conclusions

Answer 7

Credibility increases in proportion to years only for low credibility values

For larger risk : Simple Buhlmann credibility shows that double or triple the data doesn’t result in exactly double or triple credibility (since k does not change for different samples of n sizes taken from the X variable)

Z = n / (n + k)