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Test2-version1 - ACTSC 431 Loss Models 1 FALL 2007 TEST#2...

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ACTSC 431 - Loss Models 1 FALL 2007 TEST #2 Name : ID Number : 1. (12 marks) Suppose that the per payment r.v. Y p is EXP ( ° = 50) distributed. In addition, the number of payments N p has a zero-modi°ed POIS( ± = 3 ) distribution with a probability mass at 0 , p M 0 , of 0 : 2 . The actuary responsible of reviewing the previous actuary±s work decides to use a slightly di/erent model for the next period based on the claim experience : ° the per payment r.v. Y p has the same distribution ° the distribution of N p (see above) will be used instead for the number of losses N L We assume that a loss results in a (non-zero) payment with probability 0 : 9 (independently of N L ). (a) (4 marks) Prove that the new distribution for N p is a zero-modi°ed POIS ( ± = 2 : 7) with probability mass at 0 equal to 0 : 2147 . 1
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(b) (4 marks) Calculate the probability that the aggregate payment for the portfolio exceeds 100 using a normal approximation. (c) (1 marks) Discretize the distribution of Y p using the method of rounding and a span h of 15 . Calculate (to 4 decimal places of accuracy) all values up to a discretized amount paid of 30 .
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