Example F: Other Considerations - Minimum Premium

jj96gotthisjj96gotthis
edited April 2021 in W-14-Implementation

Hi,

Regarding the example in the Battlewiki for this section, I am wondering if the effect of minimum premium should be calculated as 4500/4400 -1 and the offset factor = 0.9778? We will get the final total premium = 4700.

I am thinking due to the increase in premium for the 10th policy from 200 to 300, we need the rest of the proposed premium to equal 4700 – 300 = 4400, because we need the overall premium to be 4700 (assuming this is the overall premium with a target overall rate change). This is also consistent with your calculation of $488.89 that the insurer will charge for the other 9 policies (offset factor = 488.89/500 -1 = 0.9778). Logically, I think the effect of minimum premium on base rate should only be based on the other 9 policies because the increase of $100 is distributed among the 9 policies?

Also, what if 2 out of the 10 policies did not meet the minimum premium requirement, how would the calculation for proposed base rate be done? Is it the same process of calculating effect of minimum premium and offset factor? The increase on the two policies would have to be distributed across the other 8 policies? 

If using past exam as example (2015 Fall Q11), what would the adjusted proposed base rate be if minimum premium impact NOT ONLY affects terr 1, <100k, but also terr 2, <100k?

I am actually confused on the Sample Solution 1 and 2 for that exam question...Sample solution 1 seems to use the formula of effect of minimum premium and offset factor as in Battlewiki and source text, while sample solution 2 seems to take a different approach.

Appreciate your explanation.

Thank you!

Comments

  • GrahamGraham

    Minimum premium (wiki example):

    • Your method makes more sense than the method from Werner and if this came up on the exam, you would deserve credit for your answer. It might safer however to go with Werner's method in an exam situation.

    Minimum premium (2015.Fall Q11):

    • If the $800 minimum also applied to territory 2, you would calculate the the "Prior" premium as:
    • Prior: 1684.45(.5)(.85)(1500) + 1684.45(.5)(1.0)(4000) = 4,442,737
    • And the "Proposed" premium as:
    • Prop: 800(1500) + 800(4000) = 4,400,000
    • Then calculate the amount that has to redistributed as 4,400,000 - 4,442,737 then continue as before in the solution. But of course this is negative because territory 2 is NOT subject to the minimum premium, but this is what you would do.
    • The difference between sample answer 1 and 2 is that sample answer 1 only does the minimum premium calculation for the rating cell that was subject to the minimum premium (territory 1 and AOI < 100K). But sample answer 2 calculates the "prior" and "proposed" premium for all 4 rating cells. This gives the same answer (except for rounding) but sample answer 2 is more work. This is probably the way I would have done it however because sample answer 1 takes a shortcut and when taking shortcuts, it's easier to make a mistake.
    • Note that the 3 sample answers incorporate the 15% change in different steps but since the everything is multiplicative, it doesn't matter where it's done.
    • This is a pretty good exam problem. The trick is to be methodical. There's a lot going on and you have to keep all the different steps very well organized. And I would definitely use the formulas and method from Werner for the minimum premium part rather than your alternate method.
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