Spring 2019 Q10

keshav1996keshav1996
in W-09-RiskClassification

Hi,

Please see Sample Answer 3. In it, to calculate the adj. exposures for Driver Class X and Y, they have used exposure weighted average by using Territorial relativities.

For example, exposures for Driver class X = 50*1+45*1.293+140*1.05=255 and similarly 408 for Driver class Y.

However, if we know that the exposure distribution is uniform between driver class and territory due to no exposure correlation i.e. 38% of total exposures in Driver Class X and remaining in Y, so can't we simply do 38% * Total adj territorial exposures and similarly for Y??

The exposures then become .38*848 = 326 and .62*848= 522 fro X and Y.

I know these are different than in the examiner's report but , they are leading to exactly the same answer in terms of relativities. There is something which is making them equal I suppose and this is important for me because this is what striked my mind first and maybe you can guide if it is a correct alternate approach too.

Thanks.

Comments

  • GrahamGraham

    Sample answer 3 uses a "sequential analysis", which is not on the syllabus so you should ignore this sample answer. According to the official syllabus, this is what you need to know from chapter 10:

    image.png

    You do not have to know how to perform the methods described in chapter 10. You only have to know how to interpret output results. The solution to the exam problem 2019.Spring Q10 is from chapter 9 and sample answer 1 is the best model.

  • carrotscarrots

    Hello,

    I don't understand the sample answer 1. I'm not sure how to go about it when there's a third variable, would it be possible to breakdown the sample answer 1? I found that the solutions you had for the APP practice problems were clear and I tried working this problem the same way but I get stuck at how to involve another variable. Thank you!

  • GrahamGraham

    This was question maybe a little unfair. It was different from the text examples of the adjusted pure premium approach because we aren't given the current relativities. Normally we would use the current relativities to adjust the exposures. Since we can't do that, the solution starts by observing:

    • There is no distributional bias between driver type and territory. You know this because:
    • ==> 50/80=0.625
    • ==> 45/72=0.625
    • ==>140/224=0.625

    For a review of detecting distributional bias (also called distortion), click here:

    That means you can use the unadjusted pure premium approach to calculate the relativities for driver type and territory as shown in sample answer 1. (I didn't show the driver type calculation so if you're unsure how that works, I can add more explanation.) The resulting indicated (rebased) relativities for territory are as shown in the examiner's report:

    • territory 1: 1.0
    • territory 2: 1.701
    • territory 3: 0.982

    It's these indicated relativities for territory that you then have to use in the adjusted pure premium approach to calculate the vehicle class relativities: The adjusted pure premium for vehicle class is calculated as follows:

    • vehicle class A: (30 x 1.0) + (15 x 1.701) + (200 x 0.982) = 251.95
    • vehicle class B: (80 x 1.0) + (22 x 1.701) + (104 x 0.982) = 219.57
    • vehicle class C: (20 x 1.0) + (80 x 1.701) + ( 60 x 0.982) = 215.04

    Then you use these adjusted exposures to apply the "normal" pure premium method. So you calculate the adjusted pure premium like this:

    • vehicle class A: ( 30 + 15 + 200) / 251.95 = 0.9724
    • vehicle class B: (100 + 33 + 135) / 219.57 = 1.2206
    • vehicle class C: (30 + 200 + 105) / 215.04 = 1.5578

    Then rebase these indicated relativities using vehicle class A as the base class.

Sign In or Register to comment.