claim amount increase impacts

Discussion in 'CS2' started by Molly, Apr 17, 2022.

  1. Molly

    Molly Ton up Member

    Hi all,

    I keep seeing it popping up for the pareto distribution that a claim amount increase of 5% for example would have impact only on lambda. I cant find any justification on this in the course notes, does anyone know of a rule for this?

    also, im a bit worried now that there might be rules for the other distributions that im not aware of, regarding claim amount increases - is there some sort of general rule?

    Could someone please help on this? (I understand its easter, so its a bit of a long-shot but any help would be really appreciated!)
     
    Molly, Apr 17, 2022
    #1
  2. Andrew Martin

    Andrew Martin ActEd Tutor Staff Member

    Hello

    One way to approach this is to introduce some random variables and consider CDFs. Let X be the original claim amount and let it follow the Pa(a,b) distribution.
    Let Y =1.05X then:

    P(Y <= y) = P(1.05X <= y) = P(X <= y/1.05)

    = 1 - (b/(b+y/1.05))^a
    = 1 - (1.05b/(1.05b+y))^a
    Let b'=1.05b
    FY(y) = 1 - (b'/(b'+y))^a
    This is the CDF of the Pa(b', a) distribution.

    Hope this helps!

    Andy
     
    Last edited: Apr 18, 2022
    Andrew Martin, Apr 18, 2022
    #2
  3. Molly

    Molly Ton up Member

    Hi Andy,

    thats a really interesting way of thinking about it, thank you so much thats really helpful!!!
     
    Molly, Apr 18, 2022
    #3
  4. Andrew Martin

    Andrew Martin ActEd Tutor Staff Member

    No problem! I noticed a typo in my post, I had b'=b instead of b'=1.05b, I have updated it now.
     
    Andrew Martin, Apr 18, 2022
    #4

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