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October 2010 7 (i)

Discussion in 'SP9' started by Edwin, Aug 3, 2014.

  1. Edwin

    Edwin Member

    I still can't figure out what formula is shown in the examiner's report for part (i) (a)?

    i.e
    S = \(\sum\limits_{i=1}^{k}\) \(\sum\limits_{j=1}^{N_i}\)\(X_{ij}\)

    I happened to have read too much into "Combine...." in statement (2) and suggested a formula of a Copula then went on to suggest simulating from an appropriate copula chosen based on the underlying dependence structure.

    Why am I wrong?
     
    Edwin, Aug 3, 2014
    #1
  2. Simon James

    Simon James ActEd Tutor Staff Member

    k is the number of risk categories. N is the number of risks observed in that category. S is then simply the sum of all the losses across all of the risk categories.

    As the question is about Monte Carlo simulation we should probably stick to this (ie assume losses are random from some distribution, and allow for correlations between risk categories in the model). If I was marking I may give you a mark for suggesting that a copula could be used to model dependency (if you expressed it well), but it is not the main thrust of the question.
     
    Simon James, Aug 4, 2014
    #2
  3. Edwin

    Edwin Member

    Thanks Simon,

    Can I say this to check if I understand;-

    "Copula is closed form, Monte Carlo is not."

    However I think the examiners' wording was confusing.

    Part (1);- "Adopt separate frequency and severity distributions for each risk." is the one that uses Monte Carlo to simulate via the inverse transform method.

    Part (2);- "Combine the various frequency and severity distributions into a single aggregate operational loss distribution using Monte Carlo simulation." has nothing to do with a simulation and is a SUMPRODUCT in excel.

    I'm i still dreaming?
     
    Last edited by a moderator: Aug 4, 2014
    Edwin, Aug 4, 2014
    #3
  4. Simon James

    Simon James ActEd Tutor Staff Member

    You can say it (!) - but I'm not sure what the question is :)

    That's why we recommend ActEd's ASET! :D

    Again, I'm not sure what the question is - I can use a chosen distribution to generate a random number of loss events and then sample some losses from another distribution. I then add them all up to get the total (I think its simply a SUM, not a SUMPRODUCT). Part 2 is not a simulation, but a continuation of the process. Seems a reasonable approach?
     
    Simon James, Aug 4, 2014
    #4
  5. Edwin

    Edwin Member

    Hi Simon, you're right, it's a SUM, my point is they shouldn't say results will be combined by Monte Carlo in their statement (2) in the original question.

    Thank you Simon.
     
    Last edited by a moderator: Aug 4, 2014
    Edwin, Aug 4, 2014
    #5
  6. Simon James

    Simon James ActEd Tutor Staff Member

    Ah, I see what you mean. The mention of Monte Carlo in (2) is redundant!
     
    Simon James, Aug 5, 2014
    #6

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