RelativeResourceManager3 - s ( x ) = ( -x ) for 0 x ,...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
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:
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: s ( x ) = ( -x ) for 0 x , > 0. Show that: e x = -x +1 for 0 x , > 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)...
View Full Document

Page1 / 5

RelativeResourceManager3 - s ( x ) = ( -x ) for 0 x ,...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online