Graduate Curriculum Committee Course Proposal Form
For Courses Numbered 6000 and Higher
Note: Before completing this form, please carefully read the accompanying instructions.
1. Course prefix and number:
6100
2. Date:
9/1/10
3. Requested action:
x
New Course
Revision of Active Course
Revision & Unbanking of a Banked Course
Renumbering of an Existing Course from
from
to
#
#
4. Method(s) of delivery (check all boxes that apply for both current/proposed and expected
future delivery methods within the next three years):
Current or
Proposed Delivery
Method(s):
x
On-campus (face to face)
Expected
Future Delivery
Method(s):
x
Distance Course (face to face off campus)
Online (delivery of 50% or more of the instruction is offered online)
5. Justification (must cite accreditation and/or assessment by the graduate faculty) for new course
or course revision or course renumbering:
The Graduate Faculty of the Department of Mathematics met in Spring 2010 and
assessed that an applied statistics and probability course focusing on preparation
for the Society of Actuaries exams is a needed elective in the mathematics MA
program. Risk Analysis is a key requirement for passing Actuarial Exam C. As
such, offering a course in the Mathematics of Risk Analysis would offer
mathematics graduate students another career option, and it would provide both
our students as well as the department further options in applied directions.
6. Course description exactly as it should appear in the next catalog:
6100. Mathematics of Risk Analysis (3)
P: MATH 2172,3307,3308; or consent of instructor. Single-period mathematical
risk theory is covered, including approaches to modeling and measuring
(insurance) risks. Topics include (univariate) distribution theory: exponential
dispersion models, elliptical distributions, (a,b,k) class, heavy-tailness; risk
measurement: value-at-risk, expected shortfall, coherency; policy modifications:
deductibles, (co)insurance, limits. Students are prepared to take the Society of
Actuaries Exam P “Probability” and Exam C “Construction and Evaluation of
Actuarial Models”.
Revised 09-16-09
7. If this is a course revision, briefly describe the requested change:
8. Graduate catalog page number from current (.pdf) graduate catalog:Page
Page114
114
9. Course credit:
Lecture Hours
3
3
Weekly
OR
Per Term
Credit Hours
s.h.
Lab
Weekly
OR
Per Term
Credit Hours
s.h.
Studio
Weekly
OR
Per Term
Credit Hours
s.h.
Practicum
Weekly
OR
Per Term
Credit Hours
s.h.
Internship
Weekly
OR
Per Term
Credit Hours
s.h.
Other (e.g., independent study) Please explain.
3
Total Credit Hours
10. Anticipated annual student enrollment:
10
11. Affected degrees or academic programs:
Degree(s)/Program(s)
Current Catalog Page
M.A. in Mathematics
M.B.A. in Business
M.S. in Economics
s.h.
p. 111 (pdf)
p. 164 (pdf)
p. 82 (pdf)
Changes in Degree Hours
None
None
None
12. Overlapping or duplication with affected units or programs:
Not applicable
x
Notification & response from affected units is attached
13. Council for Teacher Education (CTE) approval (for courses affecting teacher education):
Not applicable
x
Applicable and CTE has given their approval.
14. Service-Learning Advisory Committee (SLAC) approval
x
Not applicable
Applicable and SLAC has given their approval.
15. Statements of support:
a. Staff
x Current staff is adequate
Additional staff is needed (describe needs in the box below):
b. Facilities
x Current facilities are adequate
Revised 09-16-09
Additional facilities are needed (describe needs in the box below):
c. Library
x
Initial library resources are adequate
Initial resources are needed (in the box below, give a brief explanation and an
estimate for the cost of acquisition of required initial resources):
d. Unit computer resources
x
Unit computer resources are adequate
Additional unit computer resources are needed (in the box below, give a brief
explanation and an estimate for the cost of acquisition):
e. ITCS resources
x
ITCS resources are not needed
The following ITCS resources are needed (put a check beside each need):
Mainframe computer system
Statistical services
Network connections
Computer lab for students
Software
Approval from the Director of ITCS attached
16. Course information (see: Graduate Curriculum and Program Development Manual for
instructions):
a. Textbook(s) and/or readings: author(s), name, publication date, publisher, and
city/state/country
Klugman, S.A., Panjer, H.H., Wilmot, G.E., (2008), Loss Models: From Data to
Decisions (Third Edition), Wiley
Hassett, M.J., Stewart, D., (2009), Probability for Risk Management (Second Edition),
ACTEX Publications
b. Course objectives for the course (student – centered, behavioral focus)
Upon completion of the course the student will be able to:
1) model, and measure (insurance) risk;
2) apply exponential dispersion models, elliptical distributions, (a,b,k) class,
heavy-tailness;
3) apply risk analysis in insurance settings, including: Value-at-Risk, Expected
Shortfall, coherency;
4) determine and modify policy, including: deductibles, (co)insurance, limits;
5) pass the Society of Actuaries Exams P “Probability” and C “Construction
Revised 09-16-09
and Evaluation of Actuarial Models”.
c. Course topic outline
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.
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
Revised 09-16-09
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-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.
d. List of course assignments, weighting of each assignment, and grading/evaluation system
for determining a grade
Tests (3 tests)
= 50%
Final Exam
= 25%
Quizzes
= 25%
Grade in course: 100% - 90% = A; 80% - 89% = B ; 70% - 79% = C; < 70% = F
Revised 09-16-09