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# 6 ans - MATH 471 Actuarial Theory I Homework#6 Fall 2010...

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MATH 471: Actuarial Theory I Homework #6: Fall 2010 Assigned September 29, due October 13 1. Assume μ x ( t ) = μ and δ t = δ for t 0. Show: ¯ A x = μ μ + δ . 2. Z is the present value random variable for a whole life insurance of b payable at the moment of death of (x): (i) δ = 0.04 (ii) μ x ( t ) = 0.02 for t 0 (iii) The single benefit premium for this insurance is equal to var ( Z ). Calculate: b . (3.75) 3. Let Z be the present value random variable for a special continuous whole life insurance on (x), where for t 0: (i) b t = 1000 exp[0 . 05 t ] (ii) μ x ( t ) = 0.01 (iii) δ t = 0.06 (a) Calculate the actuarial present value of this insurance. (500) (b) Calculate the variance of Z . (83,333.33) 4. Let Z be the present value random variable for a whole life insurance on (x) with a benefit of 10,000 payable at the moment of death. Assume μ x ( t ) = 0.03 and δ t = 0.06 for t 0. (a) Determine the cumulative distribution function of Z . (b) Calculate the 65th percentile of the distribution of Z . (4225) ————THERE ARE MORE PROBLEMS ON THE BACK ————

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5. Let Z
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6 ans - MATH 471 Actuarial Theory I Homework#6 Fall 2010...

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