Actuarial Science Program
DEPARTMENT OF MATHEMATICS
Math 476 / 567
Actuarial Risk Theory
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Fall,
2008 |
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319
Gregory Hall |
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374 Altgeld Hall |
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Phone: 244-1739 |
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Office
Hours: or by appointment |
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E-mail: |
Required Text: Derivatives Markets by McDonald (2nd
Edition)
Daily Schedule and Assignment Postings: See Below
Course Overview
This course covers several important and
interesting actuarial topics in the areas of stochastic processes, risk
theory, and financial economics. In the first part of the course (after a
quick review of probability and statistics), we will discuss stochastic
processes, which involve the evolution of random variables over time. Specific
topics here include Markov chains, Poisson processes, and Brownian motion. This
material is critical for understanding advanced actuarial and financial
material-for example, the Black-Scholes option
pricing model. This is followed by brief discussions of two areas of
application of stochastic processes: risk theory and stochastic simulation.
In the second part of the course, we cover
certain topics in financial economics (in particular, option pricing theory)
with emphasis on mathematical modeling and understanding. Our goal is to
discuss the material on actuarial Exam 3F/MFE. Specific topics include the
basics and background of options, put-call parity, binomial option pricing, the
Black-Scholes model, and interest rate modeling.
Accessibility
Statement
To
insure that disability-related concerns are properly addressed throughout the
semester, students with disabilities who require reasonable accommodations to
participate in this class are asked to contact me within the first two weeks of
class.
Some key dates for the
class are noted below:
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August 26 (Tuesday) |
First day of class:
Introduction and Motivation |
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September 25
(Thursday) |
Exam # 1 |
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October 30 (Thursday) |
Exam # 2 |
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December 9 (Tuesday) |
Last day of class |
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December 16 (Tuesday, |
Exam # 3 (Final Exam) |
In most non-exam weeks,
there will be a homework assignment and one or more short in-class assignments.
In addition, practicing actuaries will occasionally be invited to give guest presentations
to the class during the semester.
Grading
Course grades will be
determined based on the following weights:
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Homework assignments |
20 % |
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In-class/other
assignments |
5 % |
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Group Project |
10 % |
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Exams 1 and 2 |
40 % (20% each) |
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Final Exam |
25 % |
Exams may not be made up
or taken at different times, except in extremis. In general, the grade
weight for a missed exam (provided there is a valid excuse) will accrue equally
to any remaining exams. A missed in-class or homework assignment may
not be made up. Class attendance is expected; serious attendance
problems may result in a grade lower than that indicated by the weighting
system 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.
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September 18 |
Registration deadline
for CAS Exam 3L (for Nov 2008) |
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September 24 |
Registration deadline
for Exams 2/FM, MLC, 3F/MFE, 4/C (for Nov 2008) |
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October 2 |
Registration deadline for
Exam 1/P (for Nov 2008) |
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October 28 |
CAS Exam 3L |
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November 3 |
Exam 4/C |
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November 4 |
Exams MLC and 3F/MFE |
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November 4-10 |
Computer-based Exam
2/FM |
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November 18-24 |
Computer-based Exam
1/P |
Class Summaries
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Date |
General Topic |
Specific Class Topics |
Assignments |
Textbook |
Other Items / Links |
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Aug. 26 |
Introduction and
motivation. |
Review of syllabus. Motivation via
mathematical and financial context. |
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Aug. 28 |
Review of probability
and statistics. |
Conditional
probability. Bayes formula. Distributions. |
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Sep. 2 |
Stochastic processes. |
Markov chains. |
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Sep. 4 |
Stochastic processes
(cont.). |
Markov chains (cont.). Poisson processes. |
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Sep. 9 |
Stochastic processes
(cont.). |
Poisson processes
(cont.): Interarrival and waiting times, Compound processes. |
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Sep. 11 |
Stochastic processes
(cont.). |
Brownian motion: Wiener process, Arithmetic BM, Geometric BM. |
Chapter 20.1 to 20.3. |
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Sep. 16 |
Risk and ruin theory |
Surplus and the
surplus process. Discrete probability
of ruin calculations. |
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Sep. 18 |
Simulation |
Random numbers. Inverse transform
method. |
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Sep. 23 |
Simulation (cont.) |
Inverse transform
method. Applications. |
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Sep. 25 |
Exam 1 |
In 106 and 192 Begins at One 3-inch by 5-inch notecard allowed. Any type of calculator
allowed. |
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Sep. 30 |
Option pricing theory |
Review of Exam 1. Option background. Put-call parity. |
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Chapter 9.1 |
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Oct. 2 |
Option pricing theory
(cont.) |
Put-call parity. Synthetic securities. |
Chapter 9 |
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Oct. 7 |
Option pricing theory
(cont.) |
Option pricing
relationships. Convexity. |
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Chapter 9 |
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Oct. 9 |
Option pricing theory
(cont.) |
Binomial pricing. Portfolio replication. Risk-neutral pricing. |
Chapter 10 |
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Oct. 14 |
Option pricing theory
(cont.) |
Pricing European
options with a binomial framework. |
Chapters 10 and 11 |
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Oct. 16 |
Option pricing theory
(cont.) |
Pricing American
options with a binomial framework. |
Chapters 10 and 11 |