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A5-431F08

# A5-431F08 - ASSIGNMENT 5 ACTSC 431/831 FALL 2008 Due at the...

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ASSIGNMENT 5 – ACTSC 431/831, FALL 2008 Due at the beginning of the class on Thursday, November 27 . 1. Assume that the aggregate losses in a portfolio are a collective risk model S = N i =1 X i , where N has the following pf k 0 1 2 3 4 5 Pr { N = k } 0.1 0.2 0.2 0.2 0.2 0.1 , and X 1 , X 2 , ... have the same distribution as X with the following pf k 2 4 6 Pr { X 1 = k } 1/5 3/5 1/5 . (a) Calculate the stop-loss premium E [( S - 5) + ]. [6 marks] (b) Calculate the stop-loss premium E [( S - 4 . 6) + ]. [5 marks] (c) Calculate V ar [( S - 4) + ]. [7 marks] 2. The aggregate losses for an insurer are a collective risk model S = N i =1 X i , where N has a geometric distribution NB (1 , 15), and X 1 , X 2 , ... have the same exponential distribution with mean 20. In an excess-of-loss reinsurance, a reinsurer will cover the loss N i =1 ( X i - 25) + , and in a stop-loss reinsurance, a reinsurer will cover the loss ( S - 150) + . (a) Calculate the net reinsurance premium for the excess-of-loss reinsurance. [4 marks] (b) Calculate the net reinsurance premium for the stop-loss reinsurance. [6 marks]

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