University of Texas at Austin Course Syllabus
Department of Mathematics
M 349P = M 389P: Actuarial Statistical Estimates
Fall 2011
I. Course Title: M 349P Actuarial Statistical Estimates (Unique Number 55350)
M 389P Actuarial Statistical Estimates (Unique Number 55595)
II. Location and Time: ENS 145
Tuesdays and Thursdays 11:00 am – 12:15 pm
III. Instructor: Mark M. Maxwell, PhD, ASA
Clinical Professor of Mathematics
Paul V. Montgomery Fellow of Mathematics
Actuarial Studies Program Director
Office: RLM 11.168
Office Hours: Tuesday and Thursday 8:00 am – 9:30 am
Wednesday 8:30 am – 10:30 am
Additional time by appointment (you suggest possible times) or by
chance (if I am in my office and willing).
E-mail: [email protected]
Telephone: (512) 471-7169 – Office
(412) 716-5528 – Cellular
IV. Grader or Teaching Assistant: None
V. Prerequisites: M 339J or M 389J (Probability Models with Actuarial Applications)
with a grade of ‘C-’ or better.
VI. Description of the Course: With M 339J = M 389J (Probability Models with
Actuarial Applications), this course covers the syllabus for the professional actuarial
examination on model construction - SOA Exam C / CAS Exam 4. M 339J meets with
M 389J, the corresponding graduate-course number. Offered every fall semester only.
This is a 3-credit course.
VII. Course Objectives: An introduction to modeling and important actuarial methods
useful in modeling. A thorough knowledge of calculus, probability, and mathematical
statistics is assumed. Students will be introduced to useful frequency and severity models
beyond those covered in life contingencies. The student will be required to understand
the steps involved in the modeling process and how to carry out these steps in solving
business problems. Students should be able to: 1) analyze data from an application in a
business context; 2) determine a suitable model including parameter values; and 3)
provide measures of confidence for decisions based upon the model. Students will be
introduced to a variety of tools for the calibration and evaluation of the models. Students
will work on presentation/communication skills, personal responsibility, and assessment.
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VIII. Learning Outcomes: Students will become familiar with survival, severity,
frequency and aggregate models, and use statistical methods to estimate parameters of
such models given sample data. Students will be able to identify steps in the modeling
process, understand the underlying assumptions implicit in each family of models,
recognize which assumptions are applicable in a given business application, and
appropriately adjust the models for impact of insurance coverage modifications.
Specifically, after taking both M 339J AND M 349P, students will be expected to
perform the tasks listed below:
A. Severity Models
1. Calculate the basic distributional quantities:
a) Moments
b) Percentiles
c) Generating functions
2. Describe how changes in parameters affect the distribution.
3. Recognize classes of distributions and their relationships.
4. Apply the following techniques for creating new families of distributions:
a) Multiplication by a constant
b) Raising to a power
c) Exponentiation
d) Mixing
5. Identify the applications in which each distribution is used and reasons
why.
6. Apply the distribution to an application, given the parameters.
7. Calculate various measures of tail weight and interpret the results to
compare the tail weights.
B. Frequency Models: For the Poisson, Mixed Poisson, Binomial, Negative
Binomial, Geometric distribution and mixtures thereof:
1. Describe how changes in parameters affect the distribution.
2. Calculate moments.
3. Identify the applications for which each distribution is used and reasons
why.
4. Apply the distribution to an application given the parameters.
5. Apply the zero-truncated or zero-modified distribution to an application
given the parameters.
C. Aggregate Models
1. Compute relevant parameters and statistics for collective risk models.
2. Evaluate compound models for aggregate claims.
3. Compute aggregate claims distributions.
D. For Severity, Frequency and Aggregate Models
1. Evaluate the impacts of coverage modifications:
a) Deductibles
b) Limits
c) Coinsurance
2. Calculate Loss Elimination Ratios.
3. Evaluate effects of inflation on losses.
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E. Risk Measures
1. Calculate VaR, and TVaR and explain their use and limitations.
F. Construction of Empirical Models
1. Estimate failure time and loss distributions using:
a) Kaplan-Meier estimator, including approximations for large data sets
b) Nelson-Åalen estimator
c) Kernel density estimators
2. Estimate the variance of estimators and confidence intervals for failure
time and loss distributions.
3. Apply the following concepts in estimating failure time and loss
distribution:
a) Unbiasedness
b) Consistency
c) Mean squared error
G. Construction and Selection of Parametric Models
1. Estimate the parameters of failure time and loss distributions using:
a) Maximum likelihood
b) Method of moments
c) Percentile matching
d) Bayesian procedures
2. Estimate the parameters of failure time and loss distributions with censored
and/or truncated data using maximum likelihood.
3. Estimate the variance of estimators and the confidence intervals for the
parameters and functions of parameters of failure time and loss distributions.
4. Apply the following concepts in estimating failure time and loss
distributions:
a) Unbiasedness
b) Asymptotic unbiasedness
c) Consistency
d) Mean squared error
e) Uniform minimum variance estimator
5. Determine the acceptability of a fitted model and/or compare models using:
a) Graphical procedures
b) Kolmogorov-Smirnov test
c) Anderson-Darling test
d) Chi-square goodness-of-fit test
e) Likelihood ratio test
f) Schwarz Bayesian Criterion
H. Credibility
1. Apply limited fluctuation (classical) credibility including criteria for both
full and partial credibility.
2. Perform Bayesian analysis using both discrete and continuous models.
3. Apply Bühlmann and Bühlmann-Straub models and understand the
relationship of these to the Bayesian model.
4. Apply conjugate priors in Bayesian analysis and in particular the Poisson-
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Gamma model.
5. Apply empirical Bayesian methods in the nonparametric and semiparametric cases.
I. Simulation
1. Simulate both discrete and continuous random variables using the inversion
method.
2. Estimate the number of simulations needed to obtain an estimate with a
given error and a given degree of confidence.
3. Use simulation to determine the p-value for a hypothesis test.
4. Use the bootstrap method to estimate the mean squared error of an
estimator.
5. Apply simulation methods within the context of actuarial models.
IX. Instructional Materials:
A. Textbook: Loss Models: From Data to Decisions, (Third Edition), 2008, by
Klugman, S.A., Panjer, H.H. and Willmot, G.E., ISBN 978-0-470-18781-4.
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: ACTEX Study Manual or the CSM Study Manual are
available at www.actexmadriver.com. These are optional and I recommend
AGAINST abusing study manuals. Get with some peers and obtain as many
practice problems as you are able.
D. Study Notes Available from the Society of Actuaries: See www.soa.org.
http://soa.org/files/pdf/edu-2010-spring-exam-c.pdf.
E. Other Resources: Tables for SOA Exam C/ CAS Course 4.
X: Instructor Goals for Students: In addition to mastering the mathematical content as
described in section VIII: Learning Outcomes, I hope that students 1) be positive
contributors in class, 2) are honest with self and others, 3) take responsibility for learning
the course content, 4) improve self, and 5) for those wishing to become actuaries, master
the material well enough to progress through the professional examination system and
become valuable members of the actuarial profession.
1. Behavior that I wish to encourage: honesty (with self, peers, me),
learning/understanding (e.g. defining variables, you are the audience),
discovering and challenging self and peers (names, strengths, weaknesses),
helping class, modeling productive behavior, exceeding expectations,
participation, communication, and taking responsibility (no excuses).
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2. Behavior that I wish to discourage: dishonesty (claim understand in class and
while doing homework, but not on exams), memorizing formulas, looking at
solutions prior to attempting yourself, abusing solutions manuals, use of
words “very, like, it, this, that, they, but”, ignorance, wasting the time of your
classmates, excuses, complaining, whining, and crying.
XI. Student Goals, SWOT, and Plan: See final page. Completing this page is your
first graded homework.
XII. 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).
B. Cheating: It is bad, do not do it. Cheating during an examination will result
in a letter grade of F.
C. Class Distractions: You will make the necessary arrangements so that cell
phones, 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 rare
appointment. I hope that you feel comfortable receiving help from me in a timely
manner. I will be intentionally unavailable 24 hours before a scheduled
examination. I look forward to helping those motivated students who have
attempted their homework. Bring your work into class and or office hour to
discuss your confusion.
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.
F. Professionalism: Students are expected to maintain appropriate behavior in the
classroom and other activities that reflect the actuarial program and university.
XIII: University Policies and Services
A. Honor Code: The core values of the University of Texas at Austin are
learning, discovery, freedom, leadership, individual opportunity and
responsibility. Each member of the University is expected to uphold these values
through integrity, honesty, fairness, and respect toward peers and community.
http://registrar.utexas.edu/catalogs/gi09-10/ch01/index.html
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B. Students with Disabilities:
The University of Texas at Austin provides upon request appropriate academic
accommodations for qualified students with disabilities. For more information,
students with disabilities should contact the Division of Diversity and Community
Engagement, Services for Students with Disabilities, (512) 471-6259, 471-4641
TTY. http://www.utexas.edu/diversity/ddce/ssd/
C. Accommodations for Religious Holy Days: By UT Austin policy, you must
notify me of your pending absence at least fourteen days prior to the date of
observance of a religious holy day. If you must miss a class, an examination, a
work assignment, or a project in order to observe a religious holy day, you will be
given an opportunity to complete the missed work within a reasonable time after
the absence.
D. 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/.
E. The UT Learning Center: Jester Center A332, (512) 471-3614.
F. Counseling and Mental Health Center [Crying is not permitted in RLM 11.168]
SSB 5th Floor, (512) 471-3515 Hours: Monday – Friday 8:00 a.m. – 5:00 p.m.
24-Hour Telephone Counseling: (512) 471-2255
G. Computer Labs: RLM 8.118 and RLM 7.122.
XIV: Grading Information
A. Definition of Letter Grades: I will try to minimize +/- grades, but will
assign some at my discretion. 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%]
A/A-
[80%,90%)
[70%,80%)
[60%,70%)
[0%,60%)
B+/B/BC+/C/CD+/D/DF
Achievement of distinction with an unusual
degree of intellectual initiative
Superior work
Average knowledge attainment
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
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homework problems, in-class examinations, while discussing these concepts with
others, and on the comprehensive final examination.
C. Homework: As mentioned previously, my goal is expose topics of actuarial
models to University of Texas, Austin students. I trust our goals include
demonstrating content proficiency by obtaining a passing score on SOA/CAS Exam
C/4 and improved communication skills. 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, this syllabus, and
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 announced in class.
Scoring Rubric: Your homework notebook may be collected and graded at
random times throughout the term.
D. Personal Presentations/Projects: Each student is required to submit a report
due 12/1 describing contributions to the class. The report should include a
description of your contributions and any related documentation. At least one
contribution needs to be an oral presentation (e.g. presenting a topic, solving a
homework assignment, leading a group project). If you are involved in a team
project, the team is to provide a brief description of activities of each member.
My examples of what you could contribute: Organizing and conducting study
groups, presenting a solution in class, writing sample exam questions, working in
a group to create a master answer key to textbook problems, Creating a master list
of actuarial symbols, and many other activities that you think would be useful.
Note: These projects are your responsibility. I will not give suggestions on what
you choose to do, but I am available to discuss your work before you present to
class.
D. Typical Point Scale and Examination Dates:
Pre-requisite Quiz #1
Graded Homework #1
Pre-requisite Quiz #2
Midterm Examination
Final class assessment
Accuracy of predicted Final Examination
Other
Oral Presentation
30 points
10 points
30 points
100 points
30 points
15 points
200 points
10-30 points each
50 points
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8/25
8/30
9/6
10/18
12/1
12/1
12/13
various
TBD
Second Presentation
Report on Projects
50 points
50 points
TBD
Due 12/1
Penalties:
-25 points for failure to understand this
contract
Cheating on an Examination Course grade of F.
Syllabus Understanding
Late work
25% if complete within one day
50% complete within a week, but after a day
100% if complete after one week
E. Multiplication Factor: Each student will be assessed throughout the semester
and will receive a multiplication factor (.90,1.10). Without knowing student
behavior, I would predict the normal distribution to accurately model the
distribution of multiplication factors with E[ ] 1. This factor will be
multiplied by your raw average on graded work (e.g. quizzes and exams) to
determine your course average. Examples of the multiplication factor:
a. Modeling behavior I wish to discourage, missing half of the classes,
spending class time sending text messages, copying solution manual
work for recommended homework, not participating in class,
dominating class discussion time in a wasteful manner, compromising
students secret codes, and/or I do not know your name: = .90.
b. Participation during group work, asking some questions, answering
some questions, meeting some classmates: = 1.0. I expect most
students to receive a factor quite near 1.0.
c. Modeling behavior I wish to encourage, asking intelligent questions,
using strengths and improving weaknesses, helping classmates on
group work, presenting an example in class in excess of assigned
work, organizing a helpful study session, preparing ahead of time, and
knowing everyone’s name: = 1.10.
F. Final Average: Your final class average will equal your multiplication factor multiplied by your raw average (total points you earned divided by total points
possible).
XV. 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 will model various teaching techniques including lecturing, group
projects, examinations, group work, self-inquiry, and student presentations.
XIV. 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 fall 2011 University of Texas, Austin students enrolled in M 349J = M 389J.
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Name:
Your Secret Code:
XI. Student Goals, SWOT, and Plan
A. What are your goals for this class and semester? E.g., passing with a grade of
C- so can graduate, earning an A, passing the C/4 exam in October, improving
fear of public speaking, participating in a project that can describe to potential
employers, and etcetera.
I)
II)
III)
B. List your strengths. E.g., really smart, organized, care about others, ability to
add positive integers with the use of a graphing calculator.
I)
II)
III)
C. List your weaknesses. E.g. never learned calculus, resist change, lazy, drunk,
must be the team leader in all groups because you do not trust the other students.
I)
II)
III)
D. What is your plan to accomplish your goals from section A.? E.g. attend
every class, study daily (or according to a study calendar), get off to a good start
on exams, work with students from class who can help, continue doing same thing
and hope for different results, drop this class, etcetera.
I)
II)
III)
E. Predict your multiplication factor . Your predicted multiplication factor will
be compared to the one that you earn. Accuracy will determine your grade out of
15 points.
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M 349P = M 389P Fall 2011 Course Calendar
August 22
23
24
Classes begin
29
31
30
Topic: Review of M 339J
Project: Examples of Presentations: Projects,
lectures, group work, inquiry-based, etcetera
Leader: Maxwell
Graded Homework #1 – 10 points
Last day to add or drop
5
13
14
21
Topic: B12.4– Hypothesis Testing
Project:
Leaders:
Homework:
26
28
27
4
@ UCLA (Sat 9/17)
22
23
29
@ ISU (Sat 10/1)
6
Oklahoma in Dallas 10/8
13
OK State (Sat 10/15)
5
Topic: B15.5 – Bayesian Estimation
Project:
Leaders:
Homework:
11
12
Topic: B15.5 – Bayesian Estimation
Project:
Leaders:
Homework:
17
15
Topic: B14.2 – Estimating Modified Data
(means and Variances)
Project:
Leaders:
Homework:
Topic: B15.4 – Parameter Estimation
(Greenwood’s approximation)
Project:
Leaders:
Homework:
10
BYU (Sat 9/10)
Topic: B12.4– Hypothesis Testing
Project:
Leaders:
Homework:
Topic: B15.3 – Estimating Modified Data
(means and Variances)
Project:
Leaders:
Homework:
October 3
8
Topic: B12.3 – Interval Estimation
Project:
Leaders:
Homework:
20
19
Rice (Sat 9/3)
Topic: B3.5 – VaR and TVaR
Project:
Leaders:
Homework:
Topic: B12.3 – Interval Estimation
Project:
Leaders:
Homework:
College of Natural
Science Career Fair
September 1
7
6
12
26
Topic: Review of M 339J
Project: Examples of Presentations: Projects,
lectures, group work, inquiry-based, etcetera
Leader: Maxwell
Homework:
Pre-requisite quiz #2 – 30 points
Topic:
Project:
Leaders:
Homework:
Labor Day
25
Syllabus – Change your major?
Pre-requisite quiz #1 – 30 points
Homework: student goals
Topic: B15.5 – Bayesian Estimation
Project:
Leaders:
Homework:
19
18
20
Topic: B16.2 and B 16.3 – Data and Model
Representations
Project:
Leaders:
Homework:
Midterm Examination - 100 points
21
Academic advising
CBT for C/4 October 21-27
Academic advising
25
24
26
Topic: B16.4 – Hypothesis Tests
Project:
Leaders:
Homework:
Registration begins
27
Topic: C2.4, C2.5, and C2.6
Project:
Leaders:
Homework:
Advisory Board
meeting
Kansas (Sat 10/29)
31
November 1
2
Topic: C3.1, C3.2, and C3.3
Project:
Leaders:
Homework:
7
8
9
15
16
@ Missouri (Sat 11/12)
17
Kansas State (Sat 11/19)
Topic: B20.4 – Empirical Bayes’ Theorem
Project:
Leaders:
Homework:
22
23
Topic: B21.1 – Simulation
Project:
Leaders:
Homework:
28
10
Topic: C5.2, C5.3, C5.4, and B20.3 –
Bühlmann Credibility
Project:
Leaders:
Homework:
Topic: B20.4 – Empirical Bayes’ Theorem
Project:
Leaders:
Homework:
21
Texas Tech (Sat 11/5)
Topic: C4.1, C4.2, and C4.3
Project:
Leaders:
Homework:
Topic: C5.2, C5.3, C5.4, and B20.3 – Bühlmann
Credibility
Project:
Leaders:
Homework:
14
3
25
@ Texas A&M
Thanksgiving
Thanksgiving
29
30
Topic: B21.2 – Simulating Actuarial Models
Project:
Leaders:
Homework:
December 1
Student organized final exam preparation.
Students self and class assessment – 30
points
Grade on your predicted
@ Baylor (Sat 12/3)
Last day of classes
- 15 points
Report on Projects Due – 50 points
5
M 349P = M 389P
students may choose
almost any 6 office hours
(total) 12/5 – 12/9 for me
to serve.
12
6
7
8
Final exams begin
13
M 339U final assessment, 2:00 pm
– 5:00 pm
14
Comprehensive Final Examination
200 points
9:00 am – noon
M 339 J and M 349 P
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15
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