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RelativeResourceManager3

# RelativeResourceManager3 - s x = ω-x ω α for 0 ≤ x ≤...

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MATH 471: Actuarial Theory I Homework #3: Fall 2009 Assigned September 9, due September 16 1. Let t p x = exp[ - μ * t ] for t 0 (constant force of mortality). Calculate: (a) ˚ e x . ( 1 μ ) (b) var [ T ( x )]. ( 1 μ 2 ) (c) m ( x ). ( ln( 2 ) μ ) (d) the mode of the distribution of T ( x ). (0) Note: For the above problem, I want you to derive each of the results. From this point on, memorize the answers for parts (a) and (b). 2. Let s ( x ) = 10 , 000 - x 2 10 , 000 for 0 x 100. Find the curtate expectation of life for (25). (44.5) 3. You are given: (i) e 50 = 20 and e 52 = 19.33, (ii) q 51 = 0.035 Calculate q 50 . (0.03) 4. Suppose mortality follows modiﬁed de Moivre’s Law, where:

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Unformatted text preview: s ( x ) = ( ω-x ω ) α for 0 ≤ x ≤ ω , α > 0. Show that: ˚ e x = ω-x α +1 for 0 ≤ x ≤ ω , α > 0. 5. You are given: (i) ˚ e 40 = 35 and ˚ e 40: 10 = 10 (ii) 10 p 40 = 0.85 and t p 50 = 1 - 0.01 t for 0 ≤ t ≤ 1 (iii) Improvements in mortality at age 50 cause t p 50 to change to 1 - 0.007 t for 0 ≤ t ≤ 1. Calculate the revised value of ˚ e 40 . [Hint: Use recursion formulas.] (35.07)...
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RelativeResourceManager3 - s x = ω-x ω α for 0 ≤ x ≤...

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