# 3 ans - MATH 471 Actuarial Theory I Homework#3 Fall 2010...

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MATH 471: Actuarial Theory I Homework #3: Fall 2010 Assigned September 8, due September 15 1. (a) Argue, with words, that the following is true: k +1 q x = 0 | q x + 1 | q x + ... + k | q x for k = 0, 1, 2, . ... (b) You are given: k | q 0 = 0.10 for k = 0, 1, . .., 9. Using the approach in (a), calculate: 2 p 5 . (0.6) 2. Let μ x = μ for x 0, μ > 0. 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) 3. Let s ( x ) = 10 , 000 - x 2 10 , 000 for 0 x 100. Calculate: e 25 . (44.5) 4. Suppose mortality follows modiﬁed de Moivre’s Law, where: s ( x ) = ( ω - x ω ) α for 0 x ω , α > 0. Show that: (a) ˚ e x = ω - x α +1 for 0 x ω , α > 0. (b) var [ T ( x )] = α ( ω - x ) 2 ( α +1) 2 ( α +2) for 0 x ω , α > 0. 5. You are given the following information about a new model for buildings with limiting age ω : (i) For a building aged 0: s ( x ) = ( ω - x ω ) α

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## This note was uploaded on 02/02/2011 for the course MATH 471 taught by Professor Staff during the Fall '08 term at University of Illinois, Urbana Champaign.

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3 ans - MATH 471 Actuarial Theory I Homework#3 Fall 2010...

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