MATH 471: FINAL EXAM INFORMATION Logistics:
Final Exam: Date: Thursday, December 16, 2010 Location: 149 National Soybean Research Center (1101 West Peabody Drive) Time: 8:00-11:00am (show up prior to 7:55am to take your seat and receive exam materials). C
Name: Lecture Section Time:
MATH 471: Actuarial Theory I Final Exam December 18, 2009 Exam Information and Instructions: There are 23 problems on this exam for a total of 90 points. In every problem, keep at least six decimal places during your calculatio
MATH 471: Actuarial Theory I Midterm #1 September 30, 2009 There are 6 problems on this midterm for a total of 60 points. Put your name and lecture section time on the cover of the exam booklet. Make sure that all your work is shown in the exam booklet. I
MATH 471: Actuarial Theory I Midterm #1 October 6, 2010 General Information: 1) There are 9 problems for a total of 50 points. 2) You have between 7:00-8:50pm to write the midterm. 3) You may refer to both sides of one 3in X 5in notecard. 4) You may use a
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 qx
= 0| qx + 1| qx + . + k| qx for k = 0, 1, 2, .
k | q0
(b) You are given:
= 0.10 for k = 0, 1, ., 9.
Us
MATH 471: Actuarial Theory I Homework #4: Fall 2009 Assigned September 16, due September 23 1. Fill in the missing entries for the following life table:
x 96 97 98 99 lx 10 7 3 1 px - - - - qx - - - - dx - - - 1 ex - - - -
2. You are given the following l
MATH 471: Actuarial Theory I Homework #4: Fall 2010 Assigned September 15, due September 22 1. Fill in the missing entries of the following life table:
x 96 97 98 99 lx 10 7 3 1 px qx dx 1 ex
2. You are given the following life table:
x 50 51 52 53 54 lx
SOA EXAM MLC & CAS EXAM 3L STUDY
SUPPLEMENT
by Paul H. Johnson, Jr., PhD.
Last Modied: December 2012
A document prepared by the author as study materials for the
Midwestern Actuarial Forums Exam Preparation Seminars
This document is not to be redistribute
Makeham mortality model
Parameters
A
B
c
omega
i
x
0.00022
0.00035
1.075
130
0.04
if you want to change omega or the starting age of the table,
you'll need to add or delete rows, not just type in the number
px
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
1
Math 471 - Actuarial Theory I
Assignment 4
Assignment 4 is due on Wednesday, October 19, IN CLASS.
1. (4 marks) You are given the following table of values for lx and Ax , assuming an effective
interest rate of 6% per year.
x
35
36
37
38
39
40
lx
100 000.
Math 471 - Actuarial Theory I
Assignment 1 - SOLUTION
Assignment 1 is due on Wednesday, September 7, IN CLASS.
1. (6 marks) Given the survival function
(
1
100 x, 0 x 100,
S0 (x) = 10
0,
o.w.
(a) (2 marks) Verify that this survival function satisfies the
MATH 471: Actuarial Theory I
Homework #8: Fall 2014
Assigned October 22, due October 29
AMLCR stands for the textbook Actuarial Mathematics for Life Contingent Risks. Supplement stands for SOA Exam MLC & CAS Exam
LC Study Supplement which is available as
Math 471 - Actuarial Theory I Section G1
Assignment 1
Assignment 1 is due on Wednesday, September 2, 3:00pm.
1. (7 marks) Given the survival function
S0 (x) =
1
10
100 x,
0,
0 x 100,
o.w.
(a) Verify that this survival function satises the criteria discuss
Math 471 - Actuarial Theory I Section G1
Assignment 5
Assignment 5 is due on Wednesday, October 7, 3:00pm.
1. (4 marks) When posted overseas to country A at age x, the employees of a large company
are subject to a force of mortality such that, at exact du
Math 471 - Actuarial Theory I
Assignment 3
Assignment 3 is due on Wednesday, October 5, IN CLASS.
1. (4 marks) When posted overseas to country A at age x, the employees of a large company
are subject to a force of mortality such that, at exact duration t
Notations for the EPVs of life insurances
Insurance type \ payment type
whole life insurance:
n-year term life insurance:
n-year pure endowment:
n-year endowment:
u-year deferred whole life insurance:
u-year deferred n-year term:
continuous
Ax
A1x:n
Ax:n1
Math 471 - Actuarial Theory I
Practice for Midterm 2
1. Consider contracts whose expected preset values (EPVs) are denoted by the following actuarial notations:
(i) A30
(ii) (IA(2) )30
Assume that for each contract, (30) dies at age 46.2. For each contact
Math 471 - Actuarial Theory I
Assignment 2
Assignment 2 is due on Wednesday, September 21, IN CLASS.
1. (2 marks) Given that the force of mortality follows x =
median future lifetime for (40).
1
80x
for 0 x < 80, calculate the
2. (3 marks) Given that qx+
Math 471 - Actuarial Theory I
Practice for Midterm 1
1. Explain the meanings of the following actuarial notations:
(a)
u|t q[x]+s
(b) ex:n
2. You are given that mortality follows De Moivres Law (i.e., x =
1
x )
with E(T10 ) = 50.
(a) Determine the limitin
MATH 471: Actuarial Theory I
Homework #10: Fall 2014
Assigned November 12, due November 19
AMLCR stands for the textbook Actuarial Mathematics for Life Contingent Risks. Supplement stands for SOA Exam MLC & CAS Exam
LC Study Supplement which is available
MATH 471: Actuarial Theory I
Homework #11: Fall 2014
Assigned November 19, due December 3
AMLCR stands for the textbook Actuarial Mathematics for Life Contingent Risks. Supplement stands for SOA Exam MLC & CAS Exam
LC Study Supplement which is available a
MATH 471: Actuarial Theory I
Homework #12: Fall 2014
Assigned December 3, due December 10
AMLCR stands for the textbook Actuarial Mathematics for Life Contingent Risks. Supplement stands for SOA Exam MLC & CAS Exam
LC Study Supplement which is available a
MATH 471: Actuarial Theory I
Homework #5: Fall 2014
Assigned September 24, due October 8
AMLCR stands for the textbook Actuarial Mathematics for Life Contingent Risks. Supplement stands for SOA Exam MLC & CAS Exam
LC Study Supplement which is available as
MATH 471: Actuarial Theory I
Homework #1: Fall 2014
Assigned August 27, due September 3
AMLCR stands for the textbook Actuarial Mathematics for Life Contingent Risks. You must show all work to receive full credit for any exercise.
1. Exercise 2.1 from AML
MATH 471: Actuarial Theory I
Homework #3: Fall 2014
Assigned September 10, due September 17
AMLCR stands for the textbook Actuarial Mathematics for Life Contingent Risks. Supplement stands for SOA Exam MLC & CAS Exam
LC Study Supplement which is available
Chapter 1 Introduction to life insurance
1. Life insurance:
Definition: A contract between the insurance buyer and an insurer (insurance company),
where the insurer agrees to pay certain amount of benefits upon the occurrence of an individuals or some in
Math 471 - Actuarial Theory I
Assignment 1
Assignment 1 is due on Wednesday, September 7, IN CLASS.
1. (6 marks) Given the survival function
(
1
100 x, 0 x 100,
S0 (x) = 10
0,
o.w.
(a) Verify that this survival function satisfies the criteria discussed i
Chapter 3 Life tables and selection
t px
=
lx+t
lx
t qx
=
lx lx+t
t dx
=
lx
lx
u|t qx
lx+t = lx t px
or
lx + u lx+u+t
lx
=
Fractional age assumptions: (between integer ages)
1. UDD: For an integer x and 0 s < 1
s qx
= s qx
x+s =
qx
s px
lx+s = (1 s)lx + s
Math 471 - Actuarial Theory I
Practice for Midterm 2
1. Consider contracts whose expected preset values (EPVs) are denoted by the following actuarial notations:
(i) 1000A30
(ii) (IA(2) )30
Assume that for each contract, (30) dies at age 46.2. For each con
Math 471 - Actuarial Theory I
Assignment 4
Assignment 4 is due on Wednesday, October 19, IN CLASS.
1. (4 marks) You are given the following table of values for lx and Ax , assuming an effective
interest rate of 6% per year.
x
35
36
37
38
39
40
lx
100 000.
Math 471 Actuarial Theory I
EXAM #1
Last Name:
First Name:
UIN:
Section No.: (circle one)
Date:
Time:
Total questions:
D1
G1
September 26, 2016
7:00pm - 8:20pm (80 minutes)
6
Instructions
1. Print your name and UIN in the space provided above, and make su
MATH 471 Section G1 Actuarial Theory I
Fall 2016
Syllabus
Instructor: Shu Li
Contact Info: 227B Illini Hall
Email: shuli@illinois.edu
Class Time and Location: MW, 3:00pm 4:20pm, 156 Henry Building.
Instructor Office Hours: Friday, 2:30pm 4:00pm, 227B Illi