RelativeResourceManager8 - F Y ( y ) = 0 for y <...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
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:
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

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

View Full DocumentRight Arrow Icon
Background image of page 6
This is the end of the preview. Sign up to access the rest of the document.

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) t = 0.04 for 0 < t 10, t = 0.06 for 10 < t (ii) x ( t ) = 0.06 for 0 < t 10, x ( t ) = 0.08 for 10 < t Calculate the APV. (8.95)...
View Full Document

Page1 / 6

RelativeResourceManager8 - F Y ( y ) = 0 for y <...

This preview shows document pages 1 - 6. Sign up to view the full document.

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