University of Texas, Austin Course Syllabus
Department of Mathematics
M 339V (56165) = M 389V (56505):
Actuarial Contingent Payments II
Spring 2011
I. Course Title: M 339V (56165) = M 389V (56505) Actuarial Contingent Payments II
II. Location, Days and Time: Art Building room 1.120 (ART 1.120)
Red Chalkboard, document camera, nine rows of individual stadium
seating, 90 seats.
Tuesdays and Thursdays 11:00 am – 12:15 pm
III. Faculty: Mark M. Maxwell, PhD, ASA
Clinical Professor of Mathematics
Paul V. Montgomery Fellow of Mathematics
Program Director of Actuarial Studies
Editor of the E&R section of the SOA newsletter Expanding Horizons
Office: RLM 11.168
Office Hours: Tuesday and Thursday 9:30 am – 11:00 am
Friday 9:00 am – 11:00 am
Additional hours available by appointment or by chance
E-mail: [email protected]
Telephone: (512) 471-7169 – Work
(412) 716-5528 – Cellular
IV. Grader or Teaching Assistant: None
V. Prerequisites: ACF 329: Theory of Interest and M 339U: Actuarial Contingent
Payments I with a grade of ‘C-’ or better. Pre-requisites are enforced.
VI. Description of the Course: M339V = M389V Actuarial contingent payments II. In
conjunction with M 339U (= M 389U) covers the content of SOA Exam MLC and the
"life contingencies" material on CAS Exam 3L. Topics covered: survival models,
elementary Markov Chains; life-insurance present-value random variables. Meets with
M389U, the corresponding graduate-course number. Offered every spring semester only.
This is a 3-credit course.
VII. Course Objectives: The purpose of each segment’s syllabus is to develop the
candidate’s knowledge of the theoretical basis of certain actuarial models (for life
insurance, property insurance, and annuities) and the application of those models to
insurance and other financial risks. A thorough knowledge of calculus, probability, and
interest theory is assumed. Knowledge of risk management at the level of Exam P is also
assumed.
Page -1-
The course is structured to meet the educational needs of students who major in Actuarial
Studies and/or are preparing for the SOA Exam MLC / CAS Course 3L, jointly
administered by the Society of Actuaries (SOA) and the Casualty Actuarial Society
(CAS). Our goal is to provide an understanding of the fundamental concepts of life
contingencies, and how these concepts are applied in calculating present and
accumulation values for various streams of cash flows as a basis for future use in:
reserving, valuation, pricing, asset/liability management, investment income, capital
budgeting and valuing contingent cash flows. The ultimate objective is that students
understand the learning outcomes at a high enough level in order to pass the SOA/CAS
Exam. Finally, we hope to develop study skills that will help students prepare for future
professional examinations.
VII. Course Objectives: The purpose of each segment’s syllabus is to develop the
candidate’s knowledge of the theoretical basis of certain actuarial models and the
application of those models to insurance and other financial risks. A thorough knowledge
of calculus, probability, and interest theory is assumed. Knowledge of risk management
at the level of Exam P is also assumed.
The course is structured to meet the educational needs of students who major in Actuarial
Studies and/or are preparing for the SOA Exam MLC / CAS Course 3L, jointly
administered by the Society of Actuaries (SOA) and the Casualty Actuarial Society
(CAS). Our goal is to provide an understanding of the fundamental concepts of life
contingencies, and how these concepts are applied in calculating present and
accumulation values for various streams of cash flows as a basis for future use in:
reserving, valuation, pricing, asset/liability management, investment income, capital
budgeting and valuing contingent cash flows. The ultimate objective is that students
understand the learning outcomes at a high enough level in order to pass the SOA/CAS
Exam. Finally, we hope to develop study skills that will help students prepare for future
professional examinations.
VIII. Learning Outcomes
Check the Updates section of the SOA Web site for any changes to the exam or
syllabus. Note that the learning objectives will change for the spring 2012 exam sitting.
A. Survival models
1. Define survival-time random variables
a) for one life, both in the single- and multiple-decrement models;
b) for two lives, where the lives are independent or dependent (including
the common shock model).
2. Calculate the expected values, variances, probabilities, and percentiles for
survival-time random variables.
3. Define the continuous survival-time random variable that arises from the
discrete survival-time random variable using a:
a) uniform distribution;
b) constant force of mortality; or
c) hyperbolic assumption.
Page -2-
B. Markov Chain Models
1. Define non-homogeneous and homogeneous discrete-time Markov Chain
models and calculate the probabilities of
a) being in a particular state;
b) transitioning between particular states.
C. Life insurances and annuities
1. Define present-value-of-benefit random variables defined on survival-time
random variables:
a) for one life, both in the single- and multiple-decrement models;
b) for two lives, where the lives are independent or dependent (including
the common shock model).
2. Define and calculate the expected values, variances and probabilities for:
a) present-value-of-benefit random variables;
b) present-value-of-loss-at-issue random variables, as a function of the
considerations (premiums);and
c) present-value-of-loss random variables, as a function of the
considerations (premiums).
3. Calculate considerations (premiums) for life insurances and annuities,
a) using the Equivalence Principle; and
b) using percentiles.
4. Calculate liabilities, analyzing the present-value-of-future-loss random
variables:
a) using the prospective method;
b) using the retrospective method;
c) using special formulas.
5. Calculate
a) gross considerations (expense-loaded premiums);
b) expense-loaded liabilities (reserves);
c) asset shares.
6. Using recursion, calculate expected values (reserves) and variances of presentvalue-of-future-loss random variables for general fully-discrete life insurances
written on a single life.
7. Extend the present-value-of-benefit, present-value-of-loss-at-issue, presentvalue-of-future-loss random variables and liabilities to discrete-time Markov
Chain models, to calculate
a) actuarial present values of cash flows at transitions between states;
b) actuarial present values of cash flows while in a state;
c) considerations (premiums) using the Equivalence Principle;
d) liabilities (reserves) using the prospective method.
D. Poisson processes
1. Define Poisson process and compound Poisson process.
Page -3-
2. Define and calculate expected values, variances, and probabilities for Poisson
processes,
a) using increments in the homogeneous case;
b) using inter-event times in the homogeneous case;
c) using increments in the non-homogeneous case.
IX. Instructional Materials:
A. Textbook: Actuarial Mathematics (Second Edition), 1997, by Bowers, N.L., Gerber,
H.U., Hickman, J.C., Jones, D.A. and Nesbitt, C.J., is available from the University
bookstore and is required. ISBN: 0-938959-46-8.
Chapter 3,
Chapter 4, Sections 4.1–4.4,
Chapter 5, Sections 5.1–5.4,
Chapter 6, Sections 6.1(excluding utility-theory approach), 6.2–6.4,
Chapter 7, Section 7.1(excluding utility-theory approach), 7.2–7.6,
Chapter 8, Sections 8.1–8.4,
Chapter 9, Sections 9.1–9.5, 9.6.1, 9.7, 9.9,
Chapter 10, Sections 10.1–10.4, 10.5–10.5.1, 10.5.4, 10.6
Chapter 11, Sections 11.1–11.3,
Chapter 15, Sections 15.1–15.2.1, 15.4, 15.6–15.6.1.
B. Calculator: Currently the Society of Actuaries (SOA) approves the following
calculators: Texas Instruments BA-35, BA II plus, BA II plus Professional, 30X, and/or
30Xa. It is my strongest recommendation that you donate your graphing utility to charity
and rely on the TI BA II plus professional calculator as your only calculator.
C. Other Study Materials: Visit www.actexmadriver.com or www.actuarialbookstore.com
for various study aids.
D. Study Notes Available from the Society of Actuaries: www.soa.org.
Study Notes - Life Contingencies Segment
Code Title
MLC-24-05 Multi-State Transition Models with Actuarial Applications (Second
printing with minor corrections, October 2007)
MLC-25-05 Section 8.5 from the second printing of Actuarial Mathematics, Second
Edition (to be used with text option A only) Second Printing
MLC-28-08 Poisson Processes (and mixture distributions)
Other Resources
Exam MLC Tables
http://www.soa.org/files/pdf/edu-2008-spring-mlc-tables.pdf
Candidates using the Second Edition of Models for Quantifying Risk will need to
supplement the text with the Errata Package available on the Actex web site
www.actexmadriver.com
Notational differences between Actuarial Mathematics (AM) and Models for Quantifying
Risk
Page -4-
(MQR) for candidates taking MLC
All released exam papers, since 2000 can be found here.
Exam MLC Sample Questions and Solutions
X. Delivery System: This is your class. The responsibility of learning the course
objectives (section VI.) and attaining your learning outcomes is entirely your
responsibility. I imagine the first 15 – 30 minutes of each class being devoted to
reviewing assigned homework and 45 minutes of presentation on new content.
Classes typically begin by answering homework questions posed by the students.
Maxwell Presentations: My plan is to provide a fairly traditional lectureoriented class and presenting course material at most 25% of the time. I will
provide opportunities for students to take more ownership of being exposed to
actuarial model content.
B. Student Presentations: Students (individually or in a group) wishing to
present material to the class may be allowed up to 25% of class lecture time.
Such individuals will be required to meet with me 2+ days prior to the class
presentation. Presenting, or not, will have no direct impact on your course
grade. Presenters will have the opportunity to practice public-speaking
(employers value this), to have additional access to me (for whatever that is
worth), to have more investment in course content, and have the ability to
demonstrate personal responsibility and initiative.
A.
XI. Instructor Specific Course Policies:
A.
Make-up work: Make-up work is a rare event. If you must miss a
scheduled exam, you must make alternative accommodations with me (typically
taking the exam before it is scheduled). You need to expect at most one
opportunity to complete missed work, ever.
B.
Cheating: It is bad, do not do it. Cheating during the final examination
will result in a course grade of ‘F’ and being placed on double-secret probation in
perpetuity.
C. Class Distractions: You will make the necessary arrangements so that cell
phones, pagers, watch alarms, mechanical erasers and the like do not disturb class.
D. Learning Situations Outside of Class: Following presentations in class is a
good start to understanding, being able to complete problems on your own shows
a higher level of awareness, and being able to explain solutions to others
demonstrates exceptional insight. Therefore, you are encouraged to form study
groups. I am available during class, during scheduled office hours, and by
appointment. I hope that you feel comfortable receiving help from me. I look
forward to helping those motivated students who have attempted their homework.
It is ineffective to learn a large amount of mathematics in a short period of time.
If you are having difficulty, see me immediately.
E. Extra Credit: None. Extra work is not a substitute to learning the material in
a timely fashion. It is inappropriate for you to request extra credit work.
Page -5-
F. Professionalism: Students are expected to maintain appropriate behavior in the
classroom and other activities that reflect the actuarial program and university.
G. Course Philosophy: Expectations, execution, no excuses, no exceptions. –
Tony Dungy.
XII: University Policies and Services
A. Students with Disabilities: The University of Texas at Austin provides upon
request appropriate academic accommodations for qualified students with
disabilities. For more information, contact the Office of the Dean of Students at
(512) 471-6259, 471-4641 TTY.
B. Policy on Academic Dishonesty: Students who violate university rules on
scholastic dishonesty are subject to disciplinary penalties, including the
possibility of failing in the course and/or dismissal from the University. For
further information, visit the Student Judicial Services web site at
www.utexas.edu/depts/dos/sjs/.
C. The UT Learning Center: Jester Center A332, (512) 471-3614.
D. Counseling and Mental Health Center
E. Computer Labs: RLM 8.118 and RLM 7.122.
XIII: Grading Information
A. Definition of Letter Grades:
A
B
C
D
F
Achievement of distinction with an unusual degree of intellectual
initiative. I would expect ‘A’ students to pass Exam MLC/3L.
Superior work. Students earning a ‘B’ could pass MLC/3L, but
I would think that they would have to prepare quite a bit more.
Average knowledge attainment. The Bob Beaves’ 2 things.
Unsatisfactory, but passing
Failing
B. Assessment During the Term: From the teacher - students will receive
feedback on their projects, while working in groups, during question and answer
periods, during office hours, and during competency examinations. From other
students - during study sessions and projects. From oneself – while working on
homework problems, in-class examinations, while discussing these concepts with
others, while presenting material to students, and on the comprehensive multiplechoice final examination.
C. Grade Factors: Your grade will be entirely determined by your scores
earned on pop quizzes, the in-class examinations including the mid-term and
comprehensive multiple choice final, the (up to 200 points decided, created, and
Page -6-
graded by the students) and any other graded work. If you miss graded work, then
you are responsible for the effect on your grade. No other factors enter into
determining/assigning your grade. Note that students may be adversely affected by
25-point syllabus understanding penalties. See section XIII. H.
D. Homework Notebook: As mentioned previously, my goal is expose topics of
life contingencies to University of Texas, Austin students. I trust it is our goal to
demonstrate content proficiency by obtaining a passing score on SOA Exam MLC /
CAS Exam 3L. We consider the prompt and accurate completion of homework to
be the single most important factor in student learning. It is my expectation that
students study for this class (and the professional examination) as a model for future
study. All students are to keep (and bring to class) a homework notebook of all
assigned problems. You may choose to keep some notes, other exercises, sample
examinations, projects, etcetera with the study aid.
Assigned Problems: One of your goals should be to attempt and solve all
appropriate homework problems (from this text and elsewhere). If specific
exercises will be collected, they will be noted in class.
Scoring Rubric: Your homework notebook may be collected and graded at
random times throughout the term.
E. Final Examination: The comprehensive final examination will be designed in
consultation with the actuarial faculty and knowledgeable others. Your examination
will be scored and your grade assigned based upon the following rubric:
Assigned
Grade
93-100
90-92
87-89
83-86
80-82
77-79
70-76
60-69
0
Final Exam
Score
Faculty Prediction
90% confident that student
will pass SOA/CAS exam
now
50% chance to pass
SOA/CAS now, can
eventually pass
10% chance now, 75%
eventual
50% chance of eventually
passing
25% chance of eventually
passing
10% chance of eventually
passing
No chance, some
understanding
Minimal understanding
No understanding
Cheating on the final
Uses: Data will be kept, tracked, and compared to actual professional
examination results. These results will be used to modify/improve the course,
will be components in annual reports about the program, and will be included
in a faculty member’s promotion dossier.
Page -7-
F. Typical Point Scale and Examination Dates:
Mid-Term Examination (March 10th)
100 points
Comprehensive Final Examination (May 12th)
200 points
Graded Homework (random)
25 points each
Homework Notebook
Up to 100 points
Projects (Random)
approximately 10 points each
Pop Quizzes
approximately 20 points each, up to 100 points total
Scores Produced and Graded by Students
up to 200 points total
Penalties:
Syllabus Understanding
-25 points for failure to understand this
contract
Late work
25% if complete within one day
50% complete within a week, but after a day
100% if complete after one week
G. Letter Grade Ranges: The following scale will be used to assign grades at the
end of the term. Be careful using this scale on any individually scored work. Some
examinations are easier (most students score substantially higher) than other
examinations. It is your job to maximize your total points.
[90%-100%]
[80%-90%)
[70%-80%)
[60%-70%)
[0%-60%)
A/A- range
B+/B/B- range
C+/C/C- range
D+/D/D- range
Failing
H. Syllabus Understanding Penalty: Students WILL be assessed a 25-point
syllabus understanding penalty for failure to understand this syllabus contract.
Some common examples are listed below in HOPE that you WILL NOT repeat.
1. Immaturity (e.g., acting like you are 5 years old / not following the
XI F.: Professionalism policy). Examples include pouting, crying,
whining, feeling sorry for oneself, saying “It is not fair that …”, or “It is
not my fault that …”, or “But …”
2. Not taking responsibility for YOUR actions:
a) If YOU miss a class, do NOT ask me for to provide material that
you missed including: homework assigned, representing material
to you, if there will be an unannounced pop quiz, etcetera.
b) YOUR Excuses. Common former excuses include: (1) the
student is a graduating senior, (2) the student is not a good test
taker, (3) the student has a plane ticket departing prior to a
scheduled exam, (4) the student will lose their scholarship, (5) the
student has a job lined-up, (6) student has missed class in order to
attend a job interview, 7) - ﾠ , and etcetera ad infinitum.
ﾠ
Page -8-
c) Other: Your parent contacts me. Almost anything a student does
AFTER the final examination has been given. Student asks me to
believe their fabricated stories.
I. Alternate Route to a “C-“: There is a special path for a “gift” C- grade.
The requirements (based in understanding some content) will be decided by the
class and approved by me on Tuesday January 24th. We will sign a contract.
Students will NOT be able to opt-in nor opt-out after January 26th. The student
will still be held to syllabus understanding penalties. The student will be
discouraged from attending class, will be asked to not participate in the e-survey
evaluations of the class, and asked to not hurt anybody. No other penalties will be
incurred.
XIV. Special Requirements of students registered in M 389V:
a) 1 presentation, AND
b) Leading 1 special project (e.g. Form a team the presents chapter 8, alternate
rout to C-, or keeping track of attendance {if applicable}).
XV. Changes: This syllabus is subject to modification. Any changes will be announced
in class.
©-2011 M. M. Maxwell. This syllabus is for the use of spring 2011 University of Texas, Austin students enrolled in M 339V or
M389V.
Page -9-
M339V(56165) = M389V (56505) Spring 2011 Course Calendar
January 17
Rev. Martin
Luther King Jr.
holiday
18
Spring 2011 Classes Begin
Pre-Ungraded Quiz
Syllabus and 1st Day handout
Stories
20-point pre-requisite quiz
OH 9:30A-11:00A
19
21
OH 9:00A-11:00A
Last day to add/drop
OH 9:30A-11:00A
24
25
26
Alternate Route to “C-“ deadlines (apply/requirements)
Up to 200 points student determined
A.M. § 5.2: Continuous Life Annuities
OH 9:30A-11:00A
31
20
MAXWELL
A.M. § 5.1: Introduction to Life Annuities
A.M. § 5.2: Continuous Life Annuities
27
28
A.M. § 5.3: Discrete Life Annuities
OH 9:00A-11:00A
OH 9:30A-11:00A
February 1
2
3
4
12th day of class –
A.M. § 5.4: Life Annuities with m-thly Payments
SPECIAL DAY
OH 9:00A-11:00A
OH 9:30A-11:00A
OH 9:30A-11:00A
7
8
9
A.M. § 6.1: Introduction to Benefit Premiums
A.M. § 6.2: Fully Continuous Premiums
10
11
A.M. § 6.3: Fully Discrete Premiums
OH 9:00A-11:00A
OH 9:30A-11:00A
OH 9:30A-11:00A
14
15
16
A.M. § 6.4: True m-thly Payment Premiums
17
A.M. § 7.1: Introduction to Benefit Reserves
A.M. § 7.2: Fully Continuous Benefit Reserves
18
OH 9:00A-11:00A
OH 9:30A-11:00A
OH 9:30A-11:00A
21
22
23
A.M. § 7.2: Fully Continuous Benefit Reserves
A.M. § 7.3: Other Formulas for Fully Continuous Benefit
Reserves
OH 9:30A-11:00A
28
25
OH 9:00A-11:00A
OH 9:30A-11:00A
March 1
2
A.M. § 7.4: Fully Continuous Benefit Reserves
3
A.M. § 7.5: Benefit Reserves Based on Semi-Continuous
A.M. § 7.6: Benefit Reserves Based on True
m-thly Payment Premiums
OH 9:30A-11:00A
OH 9:30A-11:00A
7
24
SPECIAL DAY
8
9
Review for Midterm Examination
10
Midterm Examination
OH 9:30A-11:00A
4
OH 9:00A-11:00A
11
No office hours
OH 9:30A-11:00A
14
15
16
17
18
21
22
23
24
25
A.M. § 8.1: Introduction to Benefit Reserves
A.M. § 8.2: Benefit Reserves for General Insurances
A.M. § 8.3: Recursion Relations for Fully Discrete
Benefit Reserves
OH 9:30A-11:00A
28
DEADLINE to register
for MLC
OH 9:00A-11:00A
OH 9:30A-11:00A
29
30
A.M. § 8.4: Benefit Reserves at Fractional Durations
31
April 1
SPECIAL DAY
OH 9:00A-11:00A
OH 9:30A-11:00A
Last day to withdraw
OH 9:30A-11:00A
Good Friday
4
5
6
A.M. § 11.1: Introduction to Multiple Decrement Theory
A.M. § 11.2: Actuarial Present Value and
Their Numerical Evaluation
OH 9:30A-11:00A
11
18
OH 9:30A-11:00A
13
14
15
A.M. § 15.4: Types of Expenses
Academic advising
for summer/fall
April 13-15,18-22
19
OH 9:00A-11:00A
OH 9:30A-11:00A
20
A.M. § 15.6: Asset Shares
A.M. § 15.4: Recursive Relations
Registration for summer
and fall semesters 4/18-4/29
8
OH 9:00A-11:00A
12
A.M. § 15.1: Introduction to Insurance Models Including
Expenses
A.M. § 15.1.2: Expense Premiums and Reserves
OH 9:30A-11:00A
7
A.M. § 11.3: Benefit Premiums and Reserves
21
22
SPECIAL DAY
OH 9:00A-11:00A
OH 9:30A-11:00A
OH 9:30A-11:00A
25
26
27
MAXWELL
J.W.D. Multi-State Models §1
OH 9:30A-11:00A
May 2
OH 9:30A-11:00A
3
4
5
Review for Final
OH 9:30A-11:00A
6
OH 9:00A-11:00A
Last Day of Class
OH 9:30A-11:00A
10
11
MLC exam
8:30A-11:30A
16
29
OH 9:00A-11:00A
J.W.D. Multi-State Models §2
9
28
J.W.D. Multi-State Models §2
17
12
13
19
20
M339V=M389V
Final Examination 2:00P-5:00P
18