Bailey.Simon
Reading: Bailey, R. A. & Simon, L. J.: "An Actuarial Note on the Credibility of Experience of a Single Private Passenger Car", plus discussion paper by Hazam, W. J.
Synopsis: To follow...
Study Tips
This is a short paper which is somewhat hard to extract the key points from the source first time round. Read the wiki article first and focus on understanding the old exam questions. There are only two or three ways the CAS can test this material but unfortunately every couple of years they try a fourth way on the exam...
Estimated study time: 4 hours (not including subsequent review time)
BattleTable
Based on past exams, the main things you need to know (in rough order of importance) are:
- fact A...
- fact B...
reference part (a) part (b) part (c) part (d) E (2018.Spring #1) E (2018.Spring #1) E (2018.Spring #1) E (2018.Spring #1) E (2018.Spring #1) E (2018.Spring #1) E (2018.Spring #1) E (2018.Spring #1)
In Plain English!
Canadian merit ratings depend on the number of full years since the insured's most recent accident, or if they have had no accidents then the number of full years since the insured became licensed.
Merit ratings of A, X, Y, and B are available and these correspond to three or more years, two years, one year, and no years since the most recent accident or since licensing respectively. Grouping A and X together is denoted by A+X and this gives the experience for two or more accident free years.
Earned premiums in the study are on-levelled to account for prior rate changes and also modified to a common basis to account for differences in premiums between the merit ratings. That is, the merit rating factor is backed out of the premiums.
Relative claim frequency is calculated using premiums rather than earned car years to avoid distortions due to higher frequency territories producing more X, Y, and B risks and consequently higher territorial premiums. The papers refer to this as correcting for maldistribution.
The data used in the paper is split into five classes labelled 1 – 5. Class 1 is broadly defined to include vehicles used for pleasure with no male operators under 25 years old. Classes 2-5 are defined much more specifically.
Each class contains two policy years of data for merit plan ratings A, X, Y, and B. The claim frequency per $1,000 of premium is calculated for each class and merit rating. These are normalized so the overall class has a relativity of 1.000.
The paper uses the following experience modification formula [math]\mathrm{Mod}=ZR+(1-Z)\cdot1[/math], where Z is the credibility and R is the ratio of actual losses to expected losses. The complement of credibility is the ratio of 1.
It's helpful to recall that experience rating attempts to measure the deviation of an individual risk from the average risk. Whereas class ratemaking is the process of finding the average. An increase in the volume of experience increases the reliability of the indication in proportion to the square root of the volume.
By setting the modification equal to the rebased claim frequency and setting R equal to the ratio of class/merit rating relative to the class, the experience modification formula can be used to solve for credibility, Z.
We can compute the credibility for merit rating plan combinations A, A+X, A+X+Y, which are claim free for 3+, 2+ and 1+ years respectively. Hence, we know [math]R=0[/math] in each of these situations. This means the experience modification formula reduces to [math]\mathrm{Mod}=1-Z[/math].