Credibility Formula

Discussion in 'SP8' started by Shillington, Feb 25, 2016.

  1. Shillington

    Shillington Member

    Hi,

    The extension of the credibility formula for general distributions with mean mu and standard deviation sigma the formula given in the notes is:
    [​IMG]

    If I take the same approach as that in the notes I don't get this formula, I get:
    [​IMG]

    Which is also consistent with the previous Poisson formula/derivation.

    How is the formula in the notes derived?
     
  2. Shillington

    Shillington Member

    Ignore this.
     
  3. Delvesy888

    Delvesy888 Member

    Hi,

    I too would like to understand how the general formula for standards for full credibility is derived. I don't want to ignore it, whether or not it is necessary to the exams.
    I feel that the approach used for the Poisson cannot be readily extended, and that some other method must be used.
    I would have been tempted to follow the approach given for severity, but this would just give the same answer as severity.

    Thanks
     
  4. Firstly, there is little discussion on non-Poisson claims frequency because the Poisson distribution is overwhelmingly the most natural distribution to consider:
    • the negative binomial is an alternative for general insurance claims, but even this is only an extension of the Poisson (as the negative binomial distribution is the Poisson/Gamma mixture distribution, see Ch3 question 3.15)
    • what other distribution would you opt for?
    I've spent a long time searching for the general proof myself. All the academic papers state that the proof is given in Mayerson et al. "The Credibility of the Pure Premium". See https://www.soa.org/files/pdf/C-21-01.pdf

    However, I've found what I believe to be the Mayerson paper (https://www.casact.org/pubs/proceed/proceed68/68175.pdf) and it only seems to discuss the full credibility for aggregate claims. Since the Mayerson paper uses a truncated series expansion to derive the non-Poisson standard for aggregate claims, perhaps a similar approach would work for frequency? You could try it and see.

    In any case, I think it's a waste of time to worry about this much further. As I say, I've spent ages searching for the proof and I've not found it... in which case I'd bet the examiners won't be able to find it either!
     
  5. Shepherd777

    Shepherd777 Member

    I have a similar problem to Shillington and would like to see the full derivation if anyone knows this?
     
  6. Hemant Rupani

    Hemant Rupani Senior Member

    Hi,
    full derivation is explained in Section 2.3 of Chapter 18.
     
  7. Katherine Young

    Katherine Young ActEd Tutor Staff Member

    See attached.
     
    Sonam Gosai and salman100 like this.

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