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SP8 - Sept 2017 Qu 2

Q

Qayanaat

Member
Hi,

I understand the solution but how does this example make sense? In reality if we had two estimates that were so different from each other (one is approximately 30k based on past experience and the other is 100 euro), we would probably try to get better estimates before allocating weights to them, no? Was the prior distribution given a mistake? Should the Prior have been ~ Normal (100k perhaps, variance)?

Thank you.
 
I'm not entirely sure which numbers you're comparing here - but anyway, bear in mind that theta is just a parameter that varies by risk, it's not the mean or anything like that. And the general principle behind credibility theory is that you're placing a certain emphasis on the past data depending on how much you 'trust' it, and that emphasis is defined by the credibility methodology you're using - in this case, the BS method. If you had severe doubts about the past data, then you'd probably choose a different method, or ignore the past data altogether!
 
Hi Ian,

I am comparing X-bar (average losses) with B (Beta) in this step: so when calculating the credibility premium per policy:
C BE = Z * X-bar + (1-Z) B

X-bar = 30k based on past experience of the risk
B = 100 euro ; it is equal to E ( mu (theta) ) = E (theta) = 100 and theta ~ N (100, 50)

Since when calculating the C BE, we are essentially placing weights on two different estimates, I thought that this example doesn't look very practical. Because we are placing weights on two estimates that are significantly different from each other; one being 30k and the other one being just a 100 euro. That's why I thought maybe the distribution given for theta was incorrect, as that would affect the value for Beta.

In practice, if we have two estimates that are so different from each other, surely we would try to get better estimates no? Or disregard one of them altogether perhaps, whichever one we thought was not reasonable.

Thank you.
 
Ah, I see what you mean now, yes. Perhaps it is a bit unlikely, yes, although you do get volatility, particularly if the business is cat exposed or long tailed. If you could get better estimates, then yes, you would - but then if you could get reliable estimates (either from the data you have or from the complement), you probably wouldn't be so inclined to use credibility rating - which is what you're suggesting in your last sentence!
 
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