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QuestionSet3 - ACTSC 431/831 QUESTION SET 3 1. A ground-up...

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ACTSC 431/831 – QUESTION SET 3 1. A ground-up model of the losses has cdf F X ( x ) = 1 - 1458000(45 + 2 x ) (90 + x ) 4 for x 0 . The insurance policy calls for an ordinary deductible of 30 to be imposed. Moreover, the number of payments N P has a logarithmic distribution with β = 7 / 4. (a) On average, how many payments will be made on this policy? (b) Show that the cdf of Y P , the amount of payment given that a payment is made, is given by F Y P ( y ) = 1 - 13824000(105 + 2 y ) 7(120 + y ) 4 for y 0 . (c) Discretize the severity distribution from part (b) using the method of rounding and an interval of size 30. Determine all values up to a discretized amount paid of 150. (d) Use the recursive formula to calculate the discretized distribution of aggregate payments up to a discretized amount paid of 150. 2. A ground-up model of the losses has cdf F ( x ) = 1 - e - ( x/ 100) 3 for x 0 . The number of losses has a negative binomial distribution with
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QuestionSet3 - ACTSC 431/831 QUESTION SET 3 1. A ground-up...

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