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Old 02-29-2020, 08:13 PM
kianalf kianalf is offline
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Unhappy ASM Manual Exercise 11.20, 2nd Edition

Problem: https://photos.app.goo.gl/vBJrwpxoVCBDh3No7

Solution: https://photos.app.goo.gl/iNLuEanroL7K4rCF7

I'm confused where it says "For losses less than 400,000, the insurance pays 3/4 of the loss." I thought the question said the policy will cover 80% of the loss as long as it's under 400,00 (8*500,000) and if the loss if greater than 400,000 they'll only pay 300,000 (policy limit). So if that's true shouldn't the answer say "For losses less than 400,000, the insurance pays 3/4 4/5 of the loss" and they should add [Pr(400,000 < X < 500,000) * 300,000] to account for losses greater than 400,000?

I think I'm misinterpreting the question and answer but I'm just not sure where.
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Old 02-29-2020, 09:18 PM
Abraham Weishaus Abraham Weishaus is offline
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I suggest you reread the discussion of coinsurance clause (page 87). The question does NOT say that 80% of the loss is paid. It says that there is an 80% coinsurance clause. Since the insurance only covers 60% of the home's value, only 75% of the requirement has been met, and the company will therefore only pay 75% of the loss. And of course, it will also never pay more than the policy limit.
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Old 03-01-2020, 12:21 PM
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gauchodelpaso gauchodelpaso is offline
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As I am a little slow in the uptake, I had trouble to understand why 400,000 was the limit. Until I graphed it (my visual half brain). It's interesting to pay attention to what happens between 300,000 and 400,000. It's hinted but I could not get it.

The way I interpret it is as follows. It's clear that for larger losses over 500,000 (seems strange but easier for getting to the point) the maximum it would be paid would be 300,000, the contracted policy limit.

For smaller losses, as the multiplier is policy limit/(80% value of house), payment=3/4 losses, almost by definition of the coinsurance clause.

And here is what explains to me why 400,000. These smallest losses are equal to the policy limit when the loss is 400,000. And that is the maximum it would be paid. So between 300,000 and 400,000, payment is 300,000.

The hint was "And of course, it will also never pay more than the policy limit." Thank you, Abe.

In summary, plotting amount of payment Y against amount of loss X, there are 2 segments. Between X=0 and X= 400,000 an inclined line with slope 3/4. Above X=400,000 a horizontal at Y=300,000.

At X=172,839.5 it's on the realm of the sloped portion and then the payment it's 3/4 of that value.

As a variation I tried a policy limit 350,000 (0.7 of value). The slope changed to 0.7/0.8 = 0.875, and again it reaches as expected, the plateau of Y=350,000 at X=400,000.

Interestingly, it seems that when we get to Lesson 11 we forget what's in Lesson 5. So much may be the different treatments of the two texts, old C, new ratemaking.

The other issue I had was the red herring of the spliced function, but I believe it makes sense to explain the limit of the house value. And it happens that the Pareto S(500,000) = 1/8. So it makes it easier. I was wondering how come the pareto was not weighted.
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Last edited by gauchodelpaso; 03-01-2020 at 12:24 PM..
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