Practice Questions 5

# Practice Questions 5 - Practice Questions 5 ACTSC 431/831...

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Practice Questions 5 – ACTSC 431/831, FALL 2011 1. The aggregate losses for an insurer is S , which has the following pdf f S ( x ) = ( 2500 /x 5 , x 5; 0 , otherwise . The premium charged by the insurer is equal to (1+ θ ) E [ S ], which is called the expected value principle, or equal to E [ S ] + α q V ar [ S ], which is called the standard deviation principle, where θ > 0 and α > 0 are constants. Determine θ and α so that Pr { S (1 + θ ) E [ S ] } = Pr ± S E [ S ] + α q V ar ( S ) ² = 0 . 95 . 2. The aggregate claims of an insurer is the collective risk model S = N i =1 X i . You are given: (a) The number of claims, N , has a negative binomial distribution NB (2 , 1 / 5). (b) The claim sizes X 1 ,X 2 ,... have the same distributions as that of X with the following probability function k 3 4 5 Pr { X = k } 1/3 1/3 1/3 . (c) The premium charged by the insurer is equal to the mean of aggregate claims plus the variance of the aggregate claims. Calculate the probability that aggregate claims will not be greater than the premium.

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Practice Questions 5 - Practice Questions 5 ACTSC 431/831...

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