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RelativeResourceManager8

# RelativeResourceManager8 - F Y y = 0 for y< =-ln(1 05 y 3...

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MATH 471: Actuarial Theory I Homework #8: Fall 2009 Assigned October 21, due October 28 1. Assume μ x ( t ) = 0.02 and δ t = 0.05 for t 0. Calculate: (a) ¯ a x . (14.29) (b) ¯ a x : 15 . (9.29) (c) 15 | ¯ a x . (5) (d) ¯ a x : 15 . (15.55) 2. Using the Illustrative Life Table, the UDD assumption in each year of age, and i = 6%, calculate: (a) ¯ a 40 . [Hint: Use Section 4.4 of the text] (14.31) (b) var a T ) for (40). [Hint: Use Section 4.4 AND rule of moments] (7.06) 3. Let Y be the present value random variable for a continuous 20-year temporary life annuity issued to (40) with payment rate of 1 per year. Assume mortality follows de Moivre’s Law with limiting age 100, and δ = 0.05. (a) Show that the cdf of Y , F Y ( y ), is such that:

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Unformatted text preview: F Y ( y ) = 0 for y < =-ln(1-. 05 y ) 3 for 0 ≤ y < ¯ a 20 = 1 for ¯ a 20 ≤ y (b) Calculate the 20th percentile of the distribution of Y . (9.02) 4. You are given: (i) ¯ A x = 0.30 (ii) ¯ A x : 20 = 0.40 (iii) i = 0.05 Calculate the actuarial present value of a 20-year certain and life annuity, with payment rate = 100 per year, that is purchased by (x). (1482.08) 5. For a continuous whole life annuity on (x) with payment rate = 1/year: (i) δ t = 0.04 for 0 < t ≤ 10, δ t = 0.06 for 10 < t (ii) μ x ( t ) = 0.06 for 0 < t ≤ 10, μ x ( t ) = 0.08 for 10 < t Calculate the APV. (8.95)...
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RelativeResourceManager8 - F Y y = 0 for y< =-ln(1 05 y 3...

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