Actuarial Science Program
DEPARTMENT OF MATHEMATICS
Math 490 / 568
Casualty Actuarial Mathematics
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Fall
2009 |
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151 Everitt Lab |
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374 Altgeld Hall |
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9:30-10:50
am TuTh |
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Phone: 244-1739 |
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Office
Hours: 3-4 pm Tues and 2-4
pm Wed, or by appointment |
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E-mail: gorvett@uiuc.edu |
Required Text: Foundations of Casualty Actuarial Science by
Casualty Actuarial Society (4th Edition)
See below for Class
Summaries (including assignment postings) and Current Events
Course Overview
This course provides an introduction to
property/casualty actuarial science by exploring its mathematical, financial,
and risk-theoretical foundations. Specific topics include risk theory, loss
reserving, ratemaking, risk classification, credibility theory, reinsurance,
financial pricing of insurance, and other special issues and applications.
These foundational concepts should be useful in any actuarial or financial
mathematics environment. Many of the readings assigned in this course appear on
one or another of the advanced professional examinations of the Casualty
Actuarial Society (CAS), in particular exams 5 and 6.
Throughout the semester, a number of practicing
casualty actuaries will be invited to speak in class on various relevant topics
and applications. In addition, real-world-type property-casualty actuarial
projects will be undertaken. Mentoring relationships with practicing actuaries
may also be organized, to provide students with insights into the realities of
the actuarial profession, and perhaps also to help with class projects or
assignments.
Accessibility
Statement
To
ensure that disability-related concerns are properly addressed throughout the
semester, students with accessibility issues who require reasonable
accommodations to participate in this class are asked to see me right away.
Honors
Projects
For
those involved in a Campus or College honors program, such as James Scholar,
you are welcomed to perform an honors project in association with this class.
Such a project would involve an opportunity for undergraduate research relevant
to actuarial science. Please let Prof. Gorvett know of your interest in the
first few weeks of the class.
Grading
Course grades will be
determined based on the following weights:
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Homework Assignments |
15 % |
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Group Project 1 |
10 % |
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Group Project 2 |
10 % |
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Other
Assignments/Exercises |
5 % |
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Exam 1 |
20 % |
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Exam 2 |
20 % |
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Final Exam (Exam 3) |
20 % |
Exams may not be made-up
or taken at different times, except in an extreme emergency. In general, the
grade weight for a missed exam (provided there is a valid excuse) will accrue
equally to any remaining exams. A missed homework or other assignment/exercise
also may not be made up. Class attendance is expected and required. Excessive
absences may result in a lower grade than that earned according to the formula
above.
Please note that the
final exam schedule is prescribed by the university; in general, instructors
are not permitted to change the final exam timing of their courses.
Graduate students taking
this class for four hours of credit will be required to complete one additional
project. Performance on this project may impact the overall grade.
Key Dates
The following are key
dates associated with this course:
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First day of class |
Tuesday, Aug. 25 |
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Exam 1 |
Thursday, Oct. 1 |
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Exam 2 |
Thursday, Nov. 5 |
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Last day of class |
Tuesday, Dec. 8 |
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Final exam (Exam 3) |
8 am, Friday, Dec. 11 |
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Sep. 17, 2009 |
Registration Deadline for
Exam 3L (Casualty Actuarial Society) in Oct. 2009 |
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Sep. 24, 2009 |
Registration Deadline
for: -Exam 4/C in Nov. 2009 -Exam 3F/MFE in Nov.
2009 -Exam MLC in Nov. 2009 |
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Oct. 8, 2009 |
Registration Deadline
for Exam 1/P in Nov. 2009 |
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Oct. 22, 2009 |
Registration Deadline
for Exam 2/FM in Dec. 2009 |
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Oct. 27, 2009 |
Exam 3L (Casualty
Actuarial Society) |
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Nov. 2, 2009 |
Exam 3F/MFE |
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Nov. 3, 2009 |
Exam MLC (Society of
Actuaries) |
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Nov. 3-9, 2009 |
Exam 4/C (CBT) |
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Nov. 18-30, 2009 |
Exam 1/P (CBT) |
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Dec. 1-8, 2009 |
Exam 2/FM (CBT) |
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Date |
General Topic |
Specific Class Topics |
Assignments |
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Other Items / Links |
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Aug 25 |
Introduction and
Overview |
Syllabus and class
overview. Insurance industry. Casualty actuaries. |
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FCAS, Ch 1 |
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Aug 27 |
Risks and Risk Theory |
Types of risks and
insurance policies. Legal environment. Surplus and risk
theory. |
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FCAS, Ch 2 |
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Sep 1 |
Economics and
Insurance Markets |
Underwiting cycle. Characteristics of
insurance markets. Macroeconomic context. |
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Boor Papers: (2) Economic Cycle |
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Sep 3 |
Loss Reserving |
Data. Loss reserving issues. Loss development
technique. |
Student current event
presentations begin next class |
FCAS, Ch 5 |
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Sep 8 |
Loss Reserving (cont.) |
Loss development
technique (cont.). |
FCAS, Ch 5 |
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Sep 10 |
Loss Reserving (cont.) |
BF and ELR techniques. Diagnostics. Reserving issues. Accounting issues. |
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CAS Statement of
Loss Reserving Principles |
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Sep 15 |
Ratemaking |
Overall concept. Pure premium method. Loss ratio method. |
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FCAS, Ch 3 |
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Sep 17 |
Ratemaking (cont.) |
Trend and development. Basic versus total
limits. Parallelogram method
for premium. |
FCAS, Ch 3 |
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Sep 22 |
Ratemaking (cont.) |
Putting together the
elements of the ratemaking process. |
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FCAS, Ch 3 |
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Sep 24 |
Risk Classification |
Concepts and
principles. Calculations of new
base rates and relativities. |
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FCAS, Ch 6 |
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Sep 29 |
Review
for Exam # 1 |
Risk classification
problems. Review for Exam # 1. |
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Oct 1 |
Exam # 1 |
151 Everitt Lab. Open book, open note. Any type of calculator. Regular class time. |
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Oct 6 |
Individual
Risk Rating |
Hand back and review
Exam # 1. Individual risk
rating. |
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FCAS, Ch 4 |
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Oct 8 |
Claims
Made Coverage |
Occurrence vs claims made. Loss triggers. Retroactive date. Tail coverage. |
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Oct 13 |
Reinsurance |
Sample problems on
claims made coverage. Reinsurance intro. Proportional vs excess. |
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FCAS, Ch 7 |
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Oct 15 |
Reinsurance
(cont.) |
Functions of
reinsurance. Reinsurance
terminology and issues. |
FCAS, Ch 7 |
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Oct 20 |
Reinsurance (cont.) |
Reinsurance
calculations. |
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FCAS, Ch 7 |
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Oct 22 |
Reinsurance (cont.) |
Reinsurance
calculations. |
FCAS, Ch 7 |
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Oct 27 |
Increased
limits factors |
Exposure rating. ILFs. |
FCAS, Ch 7 |
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Oct 29 |
Credibility |
Classical credibility. Buhlmann and Bayesian
credibility. |
FCAS, Ch 8 |
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Nov 3 |
Review
for Exam # 2 |
Go over problems as
part of review. |
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Nov 5 |
Exam # 2 |
151 Everitt Lab. Open book, open note. Any type of calculator. Regular class time. |
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Nov 10 |
Finance
and Financial Applications |
Handed back and went
over Exam # 2. Finance background. Target total rate of
return. |
FCAS, Ch 9 |
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Nov 12 |
Finance
and Financial Applications (cont.) |
CAPM applied to
insurance ratemaking. Discounted cash flow
approach to insurance ratemaking. |
FCAS, Ch 9 |
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Nov 17 |
Finance
and Financial Applications (cont.) |
Option pricing theory
as applied to insurance ratemaking. |
FCAS, Ch 9 |
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Nov 19 |
Presentation
by |
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Dec 1 |
Dynamic
Financial Analysis |
Integrated modeling of
the underwriting and investment functions of an insurer. |
FCAS, Ch 10 |
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Dec 3 |
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Holistic risk
management of a firm. |
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FCAS, Ch 10 |
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Dec 8 |
Presentation
by Allstate Insurance |
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Dec 11 |
Final Exam |
151 Everitt Lab. Open book, open note. Any type of calculator. 8-10 am. |
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Date |
Current Event Topic |
Link (if available) |
Comments / Issues |
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Aug
25 |
More Energy Firms Go Uninsured -
WSJ, 8/24/09, p. B2. |
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Many companies involved with Gulf coast energy (including offshore oil rigs) are
going self-insured this hurricane season. -
Rate increases and/or drops in insurance coverage availability are causes. -
But enhanced regulation and technology since Hurricane Katrina may aid risk
management and promote loss reduction. |
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Sep
1 |
Insuring
your fantasy sports investment |
http://fantasysportsinsurance.com |
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Claim that their product will protect your investment in a fantasy sports
league in the event of key player injury. -
(Appearance on this class website does not represent an endorsement of the
product.) |
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Sep
1 |
Hospitals
Own Up to Errors -
WSJ, 8/25/09, p. D1 |
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Some hospitals are hoping to reduce lawsuits over medical errors by being
more open about those errors. -
Communicating and working with the families. -
A variety of safety measures are being considered and adopted. |