Average accident date for PREMIUM liabilities

user10_Exam6Cuser10_Exam6C
in CIA.PrLiabs

Wondering if the 1/3 can be explained a little further, and why it differs from claim liability accidents occurring at 1/2 of the exposure period.

Thank you!

Let me know if the above question does not make sense.

Comments

  • javidjavid

    I'll refer to page 8 of this document: https://www.cia-ica.ca/docs/default-source/2016/216076e.pdf.

    I'll try to give an example below to illustrate the idea. Let's picture one person starting on Jan 1 of a year with $1 of premium.

    For the claims side, if you assume accidents occur uniformly in the given accident year, the avg date will be 1/2 of the exposure period.

    For the premium side, if the accident date was Jan 1, there will be $1 of unearned premium to "back" this accident. If it occurred mid year, $0.50 of unearned premium. If it occurred end of year, $0 of unearned premium.

    So the unearned premium "backing" the given accident changes over time. If we want the average accident date on the premium side, we take a weighted average. Since it is a continuous function, it becomes the integral in the paper.

    Let me know if this makes sense.

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