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Math Help - Somewhat simple actuary question about filing claims.

  1. #1
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    Cool Somewhat simple actuary question about filing claims.

    Under an insurance policy, a maximum of …five claims may be filed per year by a policyholder. Let p_n be the probability that a policyholder files n claims during a given year, where n = 0,1,2,3,4,5. An actuary makes
    the following observations:

    (a) p_n >= p_{n+1} for n = 0, 1, 2, 3, 4.
    (b) The difference between  p_n and p_{n+1} is the same for n = 0, 1, 2, 3, 4.
    (c) Exactly 40% of policyholders file fewer than two claims during a given year.

    How would you calculate the probability that a random policyholder will …file more than three claims during a given year?
    Last edited by Intsecxtanx; November 5th 2009 at 07:47 AM.
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  2. #2
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    The constraints imply that the shape of the distribution must be trapezoidal.
    You need to find the 2 key values on the y-axis to get the pdf, say k1 and k2.

    Now you have 2 equations and 2 unknowns: 1 equation is provided by the fact that the total probability=1.
    The 2nd is provided by constraint (c).

    Solve simultaneously for k1 and k2.
    Now the required probability is f(4) + f(5) where f is the pdf.
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  3. #3
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    Thanks
    Last edited by Intsecxtanx; November 5th 2009 at 02:36 PM.
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