MATH 472/567
Actuarial Theory II/Topics in Actuarial Theory I
Midterm #2
April 2, 2014
General Information:
1) There are 8 problems for a total of 40 points.
2) You have between 3:00-4:20pm to write the midterm.
3) You may refer to both sides of one 3in X
MATH 472/567: Actuarial Theory II/Topics in Actuarial Theory I
Midterm #1 Additional Problems: Spring 2012
1. For a fully continuous 5-year endowment insurance of 1000 on (x) with
annual benet premium rate P :
(i) x (t) = 0.01 for t > 0
(ii) = 0.05
(a) Pr
SOA EXAM MLC & CAS EXAM LC STUDY
SUPPLEMENT
by Paul H. Johnson, Jr., PhD.
Last Modied: January 2014
A document prepared by the author as study materials for the
Midwestern Actuarial Forums Exam Preparation Seminars
This document is not to be redistributed
MATH 472/567:
Actuarial Theory II/Topics in Actuarial Theory I
Homework #6: Spring 2015
Assigned March 4, due March 11
AMLCR stands for the textbook Actuarial Mathematics for Life Contingent Risks. Supplement stands for SOA Exam MLC & CAS Exam
LC Study Su
MATH 472/567: FINAL EXAM INFORMATION
Logistics:
Final Exam:
Date: Friday, May 15, 2015
Time: 1:30-4:30pm (show up prior to 1:30pm to take your seat and receive exam
materials).
Location: 151 Everitt Laboratory
Conflict Final Exam:
Date: Wednesday, May
MATH 472/567:
Actuarial Theory II/Topics in Actuarial Theory I
Midterm #2
April 1, 2015
General Information:
1) There are 8 problems for a total of 40 points.
2) You have between 2:00-3:20pm to write the midterm.
3) You may refer to both sides of one 3in
MATH 472/567:
Actuarial Theory II/Topics in Actuarial Theory I
Homework #11: Spring 2015
Assigned April 22, due April 29
AMLCR stands for the textbook Actuarial Mathematics for Life Contingent Risks. Supplement stands for SOA Exam MLC & CAS Exam
LC Study
MATH 472/567:
Actuarial Theory II/Topics in Actuarial Theory I
Homework #10: Spring 2015
Assigned April 15, due April 22
AMLCR stands for the textbook Actuarial Mathematics for Life Contingent Risks. Supplement stands for SOA Exam MLC & CAS Exam
LC Study
MATH 472/567:
Actuarial Theory II/Topics in Actuarial Theory I
Homework #7: Spring 2015
Assigned March 11, due March 18
AMLCR stands for the textbook Actuarial Mathematics for Life Contingent Risks. Supplement stands for SOA Exam MLC & CAS Exam
LC Study S
MATH 472/567:
Actuarial Theory II/Topics in Actuarial Theory I
Homework #12: Spring 2015
Assigned April 29, due May 6
AMLCR stands for the textbook Actuarial Mathematics for Life Contingent Risks. You must show all work to receive full credit for any exer
MATH 472/567:
Actuarial Theory II/Topics in Actuarial Theory I
Homework #8: Spring 2015
Assigned March 18, due April 8
AMLCR stands for the textbook Actuarial Mathematics for Life Contingent Risks. Supplement stands for SOA Exam MLC & CAS Exam
LC Study Su
MATH 472/567
Actuarial Theory II/Topics in Actuarial Theory I
Midterm #1
February 26, 2014
General Information:
1) There are 8 problems for a total of 40 points.
2) You have between 3:00-4:20pm to write the midterm.
3) You may refer to both sides of one 3
MATH 472/567
Actuarial Theory II/Topics in Actuarial Theory I: Final Exam
May 15, 2014
General Information:
1) There are 10 problems for a total of 50 points.
2) You have between 7:00-10:00pm to write the midterm.
3) You may refer to both sides of one 8.5
MATH 472/567:
Actuarial Theory II/Topics in Actuarial Theory I
Homework #2: Spring 2015
Assigned January 28, due February 4
AMLCR stands for the textbook Actuarial Mathematics for Life Contingent Risks. Supplement stands for SOA Exam MLC & CAS Exam
LC Stu
MATH 472/567:
Actuarial Theory II/Topics in Actuarial Theory I
Homework #4: Spring 2015
Assigned February 11, due February 18
AMLCR stands for the textbook Actuarial Mathematics for Life Contingent Risks. Supplement stands for SOA Exam MLC & CAS Exam
LC S
MATH 472/567:
Actuarial Theory II/Topics in Actuarial Theory I
Homework #3: Spring 2015
Assigned February 4, due February 11
AMLCR stands for the textbook Actuarial Mathematics for Life Contingent Risks. Supplement stands for SOA Exam MLC & CAS Exam
LC St
MATH 472/567:
Actuarial Theory II/Topics in Actuarial Theory I
Homework #5: Spring 2015
Assigned February 18, due March 4
AMLCR stands for the textbook Actuarial Mathematics for Life Contingent Risks. Supplement stands for SOA Exam MLC & CAS Exam
LC Study
MATH 472/567:
Actuarial Theory II/Topics in Actuarial Theory I
Homework #1: Spring 2015
Assigned January 21, due January 28
AMLCR stands for the textbook Actuarial Mathematics for Life Contingent Risks. Supplement stands for SOA Exam MLC & CAS Exam
LC Stu
MATH 472/567:
Actuarial Theory II/Topics in Actuarial Theory I
Homework #9: Spring 2015
Assigned April 13, due April 15
AMLCR stands for the textbook Actuarial Mathematics for Life Contingent Risks. Supplement stands for SOA Exam MLC & CAS Exam
LC Study S
MATH 472/567:
ACTUARIAL THEORY II/TOPICS IN ACTUARIAL THEORY I
SPRING 2015: CLASS PROJECT INFORMATION (Due May 4)
Background
An insurer is planning to issue 15-year disability income policies. Each of these policies has the
following features:
The policy
MATH 472/567:
Actuarial Theory II/Topics in Actuarial Theory I
February 25, 2015
General Information:
1) There are 8 problems for a total of 40 points.
2) You have between 2:00-3:20pm to write the midterm.
3) You may refer to both sides of one 3in X 5in n
MATH 567: TOPICS IN ACTUARIAL THEORY I
SPRING 2015
-INSTRUCTOR:
Name:
Office:
Office phone number:
E-mail address:
Paul H. Johnson, Jr.
361 Altgeld Hall
(217)-244-5517
pjohnson@illinois.edu
Website:
http:/www.math.uiuc.edu/~pjohnson/
Office Hours: Monday
Math 472/567 Actuarial Theory II
Chapter 7 Policy Values
(1)
Shu Li
Department of Mathematics
University of Illinois at Urbana-Champaign
Spring 2016
Chapter 7 Policy values
Topics covered: Prospective loss random variables, recursions,
Thieles dierential
Example (1): Consider a fully continuous whole life insurance issued to (x) with (level) premium
rate P .
Solution. The prospective loss r.v. Lt is dened as
Lt = P V@t (future benets) P V@t (future premiums)
= v Tx t P a Tx t ,
for Tx > t.
The expectation
Math 472/567 Actuarial Theory II
Chapter 7 Policy Values
(2)
Shu Li
Department of Mathematics
University of Illinois at Urbana-Champaign
Spring 2016
Review
Prospective loss random variable at time t:
Lt =PV@t (future benets) + PV@t (future expenses)
PV@t
Math 472 / Math 567 - Actuarial Theory II
Assignment 3
Assignment 3 is due on Wednesday, February 17, 2:00pm.
Note: Exercises are all from the Second Edition of the textbook.
1. (4 marks) Exercise 7.3 (f-i).
Solution:
(f) The formula for the asset share a
Math 472 / Math 567 - Actuarial Theory II
Assignment 5
Assignment 5 is due on Wednesday, March 9, 2:00pm.
Note: Exercises are all from the Second Edition of the textbook.
1. (4 marks) Consider the Disability Income Insurance Models. You are given:
02
10
1
Math 472 / Math 567 - Actuarial Theory II
Assignment 6
Assignment 6 is due on Wednesday, March 16, 2:00pm.
Note: Exercises are all from the Second Edition of the textbook.
1. (4 marks) Consider the permanent disability model. You are given:
01
x = 0.05,
0
Math 472 / Math 567 - Actuarial Theory II
Assignment 7
Assignment 7 is due on Wednesday, March 30, 2:00pm.
Note: Exercises are all from the Second Edition of the textbook.
1. (4 marks) Exercise 8.6.
(a)
i. We have
00
10 p30
10
Z
02
(01
30+t + 30+t )dt
0
Z
Math 472 / Math 567 - Actuarial Theory II
Practice Questions 2
Note: Exercises are all from the Second Edition of the textbook.
1. Exercise 8.16.
Solution:
(a) The independent probabilities of death are
(1)
(1)
(1)
q39 = 0.00049, q40 = 0.00053, q41 = 0.00