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Soa 150

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  • Soa 150

    An automobile insurance company issues a one-year policy with a deductible of 500.
    The probability is 0.8 that the insured automobile has no accident and 0.0 that the automobile has more than one accident. If there is an accident, the loss before application of the deductible is exponentially distributed with mean 3000.
    Calculate the 95th percentile of the insurance company payout on this policy.

    Here's what I did,

    let c be the cut off point where F(c) = 0.95
    F(c) - F(500) / F(500) = 0.95 and solve for c
    i get c equal to 9487.1968 and i subtract 500 off since there is 500 deductible, and I get 8987.

    I know I have to multiply the 0.2 for the probability of accident, but I'm not sure where it would fit it. Could anyone give me some hints or explain the way they did it in the solution. Thanks!

    Here's the link to the solution and question:
    Last edited by bevele; July 26 2010, 12:08 AM.