Assignment 3

Assignment 3 - FIN 3220A Actuarial Models I First Term...

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1 FIN 3220A Actuarial Models I First Term 2005-2006 Assignment 3 Hand in the solutions on or before 16 November 2005. 1. A 3-year life annuity-due to ( x ) is defined by the following table: Year t Amount of Payment p x + t 0 1 0.80 1 2 0.75 2 3 0.50 You are given that v = 0.9 and that the expected present value of the payments is K . Calculate the probability that the present value of the payments actually made will exceed K . 2. For a 3-year temporary life annuity-due on (30), you are given: () 1 , 0 80. 80 x sx x =− ≤ ≤ i = 0.05. 1 3 0,1,2, 3, 4,5, K aK Y + = = = ±± . Calculate Var( Y ). 3. You are given: ( ) 4 17.287. a = 0.1025. x A = Deaths are uniformly distributed over each year of age. Calculate ( ) 4 x a . 4. Denote Z as the present value random variable for a special benefit on (30). This benefit provides the following: A life income of 1,000 per year payable continuously while (30) survives. An insurance of 5,000 payable at the moment of death of (30).
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Assignment 3 - FIN 3220A Actuarial Models I First Term...

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