Math 472 HW 3 Solutions

# Math 472 HW 3 - 1 4 Consider a fully discrete 5-year endowment insurance of 5000 on(40(i The annual level beneﬁt premium is 843.07(ii Mortality

This preview shows pages 1–10. Sign up to view the full content.

MATH 472/567: Actuarial Theory II/Topics in Actuarial Theory I Homework #3: Spring 2011 Assigned February 2, due February 9 1. Suppose: (i) Mortality follows the Illustrative Life Table. (ii) i = 0.06 (iii) Deaths are uniformly distributed within each year of age. Calculate: 5000 9 . 3 V 1 45: 20 . (189.67) 2. Re-do Problem 1, except calculate: 5000 9 . 3 V (12) 1 45: 20 . You may use anything that you calculated in Problem 1 along with the α ( m ), β ( m ) handout. (164.83) 3. (a) Using the following formula for h + s V for h = 0, 1, . .. and 0 < s < 1: h + s V = v 1 - s b h +1 × 1 - s q x + h + s + v 1 - s h +1 V × 1 - s p x + h + s , show that assuming a constant force of mortality between integer ages (refer to Table 3.6.1 of the text) results in h + s V equaling: v 1 - s [ b h +1 - p 1 - s x + h ( b h +1 - h +1 V )]. (b) Now consider a general fully discrete life insurance on (x), where: (i) The death beneﬁt for the 11th year is 10. (ii) The terminal beneﬁt reserve for the 11th year is 43. (iii) δ = 0.06 (iv) q x +10 = 0.10 Calculate the beneﬁt reserve at time 10.5 assuming a constant force of mortality between integer ages. (40.09) ————THERE ARE MORE PROBLEMS ON THE BACK ————

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

View Full Document

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

View Full Document

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

View Full Document

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 4. Consider a fully discrete 5-year endowment insurance of 5000 on (40): (i) The annual level beneﬁt premium is 843.07. (ii) Mortality follows the Illustrative Life Table. (iii) i = 0.06. Calculate: var [ 3 L | K (40) = 3 , 4 ,... ]. (3872.01) 5. For a fully discrete 3-year term insurance of 1000 on (x) with annual level beneﬁt premiums: (i) i = 0.10 (ii) The mortality rates and terminal beneﬁt reserves are given by: h q x + h h +1 V 0.3 95.833 1 0.4 120.833 2 0.5 (a) Determine the annual level beneﬁt premium. (333.71) (b) Calculate L assuming (x) dies: (1) in the ﬁrst year, (2) in the second year, (3) in the third year, and (4) after the third year. (575.38, 189.36, -161.57,-912.88) (c) Calculate var [ L ] using: (1) var [ L ] = E [ L 2 ]-E [ L ] 2 and (2) the Hattendorf Theorem. Round your ﬁnal answers to the nearest integer. (289,844) 2...
View Full Document

## This note was uploaded on 05/18/2011 for the course MATH 472 taught by Professor Zhu during the Spring '08 term at University of Illinois, Urbana Champaign.

### Page1 / 10

Math 472 HW 3 - 1 4 Consider a fully discrete 5-year endowment insurance of 5000 on(40(i The annual level beneﬁt premium is 843.07(ii Mortality

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online