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Thread: Loss Triangle

  1. #1
    Actuary.com - Level I Poster
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    Loss Triangle

    What is "Loss Triangle"? Thanks.

  2. #2
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    The idea is that on some kinds of insurance (e.g., health), the claims are paid over time, possibly a period of months or even years. The triangle helps you estimate how much you need to set aside as a reserve for claims that you know about but aren't finished paying for.

    The reason it's called a triangle is because you know more and more about older claims as time goes on. As you fill in your loss data, if your incurred date is on the left axis and the paid date goes along the horizontal axis, a triangle develops.

    For example, you might have a triangle that looks like this:


    Total Cumulative Claims Paid
    Months since incurred
    Incurred 1 2 3 4 5 6
    Jan 20 30 35 37 38 39
    Feb 22 32 36 39 42
    Mar 21 31 34 38
    Apr 19 26 15
    May 25 37
    Jun 18


    The actuary will use the data above, plus judgement, to determine how to "complete the triangle" (e.g., what number goes after the 42 in February claims) and determine appropriate reserves. The actuary might decide that the month 6 cumulative total is the final number, and the month 6 total should be 2x the month 1 total (or 3% higher than the month 5 total or something else) and fill in the blanks.
    Last edited by FSA; September 12th 2006 at 02:24 AM.

  3. #3
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    Thanks for explanation!

  4. #4
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    Hey guys,

    I'm just going over some questions before my semester starts (in Australia) and can't figure out this one on loss triangles.

    Basically you're given a loss triangle with respect to Underwriting year and incurred claims and are asked to come up with a way to convert this to a loss triangle with respect to ACCIDENT year and incurred claims.

    I'm totally lost and don't have the answers with me .

    Does anybody have any ideas on it?

    Thanks
    Last edited by speed2; January 26th 2009 at 10:07 PM.

  5. #5
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    Quote Originally Posted by speed2 View Post
    Hey guys,

    I'm just going over some questions before my semester starts (in Australia) and can't figure out this one on loss triangles.

    Basically you're given a loss triangle with respect to Underwriting year and incurred claims and are asked to come up with a way to convert this to a loss triangle with respect to ACCIDENT year and incurred claims.
    Hi, first post here, and I'm not an actuary (but I might play one on TV...)

    Basically, the AY claims will lag the UY claims. How much depends on the distribution of policy effective dates and claims in a calendar year, but, knowing nothing else and assuming equal distribution of each, a given AY will have about half the claims from the current UY plus half from the prior UY.

  6. #6
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    Hi Speed2:

    I think FSA explained it very well. Basically, when you develop losses by Accident Year all the accident wouldn't be reported in the first CY but as time passes by all losses will be reported (will get ultimate losses eventually) . The Loss Triangle is the way to develop those losses by ages (CY). Hope it helps.

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