Chapter 4 Question 4.6

Discussion in 'CT6' started by mcallist, Jul 13, 2017.

  1. mcallist

    mcallist Member

    Hi,

    Could someone please explain the substitution in this question and where the 5dy comes from?

    Many thanks,
    Tom
     
    mcallist, Jul 13, 2017
    #1
  2. Bharti Singla

    Bharti Singla Senior Member

    X is the random variable of total claim amount and Y is the random variable of claim amt. paid by the reinsurer. Here,
    X~Gamma(a,L)
    Retention limit is 80%, means the reinsurer is paying 20% proportion of each claim. So, Y= 0.20 X
    Take the pdf of gamma dist. and substitute Y= 0.20X → X= 1/0.20 Y → X= 5Y
    and so, dx= 5dy.
    Try by yourself, you will get it.
     
    Bharti Singla, Jul 13, 2017
    #2
    Sunil Sanga, mcallist and John Lee like this.
  3. mcallist

    mcallist Member

    Thanks a lot Bharti :)
     
    mcallist, Jul 17, 2017
    #3
    Bharti Singla likes this.

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