Mathematics 383, Actuarial Models II, Fall 2008

Illinois State University – Mathematics Department

Instructors

Classes Meet

Tuesdays and Thursdays 4:00-5:50 p.m. (with a ten minute break), in Williams Hall, room 111.

Office Hours

Office hours will be held Tuesdays and Thursdays 3:00-3:50 p.m., in Stevenson Hall room 313G, by Dr. Krzysztof Ostaszewski. Please ask for an appointment at other times.

Textbooks

Notes for all topics with practice exercises will be posted as links next to dates of classes, see below, in the schedule of classes. Links to

• Derivatives Markets, Second Edition, by McDonald, R.L., Addison-Wesley, Pearson Education, 2006.
The following (downloadable as PDFs) study notes from the Society of Actuaries are also useful:

• Multi-State Transition Models with Actuarial Applications by J. Daniel. This is a reference on Markov Processes.

• Poisson Processes (and mixture distributions), by J. Daniel. This is a reference on Poisson Processes.

• Exam MFE Introductory Study Note.

• Exam MFE Tables.

• Some Remarks on “Derivatives Markets”, by E. Shiu.

• “Derivatives Markets,” Errata, by R. McDonald.
• Exam MFE Sample Questions and Solutions.

• Exam MFE Additional Sample Questions and Solutions.

• May 2007 SOA Exam MFE and Solutions.

Objective

The objective of this class is to help you learn about Poisson and Markov stochastic processes and mathematical models utilized in financial economics.These actuarial models form a key part of modern actuarial science.

Grading

There will be a total of six tests. Any of the comprehensive tests (as indicated in the schedule) can count as a final. Because there will be so many opportunities for testing and only the best four test scores will affect the class grade, no make-up tests will be offered. The final will count as 40% of your grade, and the best two of the remaining tests will count as 30% of your grade each. You will also receive up to 20% extra credit for the best of the remaining tests. The grading scale for undergraduate students will be as follows: 80% or better — A, 70% to 80% — B, 60% to 70% — C, 50% to 60% — D, below 50% — F. The grading scale for graduate students will be: 90% or better — A, 80% to 90% — B, 70% to 80% — C, 60% to 70% — D, below 60% — F.

Important dates

Illinois State University withdrawal information for the Fall 2008 semester is given at this web site: http://www.registrar.ilstu.edu/crd/withdrawal/withdrawfall.shtml.

Disability concerns

Illinois State University provides a welcoming atmosphere for individuals with disabilities by assisting each in functioning independently within the University community and providing equal access and opportunity in accomplishing educational, professional and personal goals. Disability Concerns, a unit of the Student Affairs Division,  is the designated office to provide approved accommodation services for students, faculty, staff, and guests with disabilities. Disability Concerns obtains and maintains documentation of disability, certifies eligibility for services, determines reasonable accommodations, and develops plans for providing such accommodations. This is accomplished in a confidential manner to ensure equal opportunity for participation in all courses, programs, activities and employment offered by Illinois State. Please contact the Disability Concerns in Fell Hall room 350, tel.  309-438-5853 (Voice), 309-438-8620 (TTY) if you have needs that can be accommodate by that office.

Schedule of classes

• Tuesday, August 19, 2008. Markov Processes.
• Thursday, August 21, 2008. Markov Processes.
• Tuesday, August 26, 2008. Markov Processes.
• Thursday, August 28, 2008. Poisson Processes. Class taught by Mr. Ken Williams.
• Tuesday, September 2, 2008. Poisson Processes. Class taught by Mr. Ken Williams.
• Thursday, September 4, 2008. Poisson Processes. Class taught by Mr. Ken Williams.
• Tuesday, September 9, 2008. Parity and Other Option Relationships (Derivatives Markets, Chapter 9). Class taught by Mr. Ken Williams.
• Thursday, September 11, 2008. Parity and Other Option Relationships (Derivatives Markets, Chapter 9). Class taught by Mr. Ken Williams.
• Tuesday, September 16, 2008. Parity and Other Option Relationships (Derivatives Markets, Chapter 9). Class taught by Mr. Ken Williams.
  • Put-call parity charts.
• Thursday, September 18, 2008. Test No. 1, on the material covered through September 16, 2008.
• Tuesday, September 23, 2008.  Binomial Option Pricing I (Derivatives Markets, Chapter 10).
• Thursday, September 25, 2008. Binomial Option Pricing I (Derivatives Markets, Chapter 10).
• Tuesday, September 30, 2008. Binomial Option Pricing II (Derivatives Markets, Chapter 11).
• Thursday, October 2, 2008. Binomial Option Pricing II (Derivatives Markets, Chapter 11).
  • Additional exercises.
• Tuesday, October 7, 2008. Test No. 2, on the material covered through October 2, 2008.
• Thursday, October 9, 2008. The Black Scholes Formula (Derivatives Markets, Chapter 12).
• Tuesday, October 14, 2008. The Black Scholes Formula (Derivatives Markets, Chapter 12).
• Derivation of Black-Scholes Formula.
• Thursday, October 16, 2008. Market-Making and Delta-Hedging (Derivatives Markets, Chapter 13).
• Tuesday, October 21, 2008. Market-Making and Delta-Hedging (Derivatives Markets, Chapter 13).
• Thursday, October 23, 2008. Exotic Options (Derivatives Markets, Chapter 14). Class taught by Mr. Ken Williams.
• Tuesday, October 28, 2008. Exotic Options (Derivatives Markets, Chapter 14). Class taught by Mr. Ken Williams.
• Thursday, October 30, 2008. Brownian Motion and Ito’s Lemma (Derivatives Markets, Chapter 20). Class taught by Mr. Ken Williams.
• Tuesday, November 4, 2008. Brownian Motion and Ito’s Lemma (Derivatives Markets, Chapter 20). Class taught by Mr. Ken Williams.
• Thursday, November 6, 2008. Brownian Motion and Ito’s Lemma (Derivatives Markets, Chapter 20). Class taught by Mr. Ken Williams.
• Tuesday, November 11, 2008. Interest Rate Models (Derivatives Markets, Chapter 24).
• Thursday, November 13, 2008. Interest Rate Models (Derivatives Markets, Chapter 24).
• Tuesday, November 18, 2008. Interest Rate Models (Derivatives Markets, Chapter 24).
• Thursday, November 20, 2008. Test No. 3, comprehensive.
• Tuesday, December 2, 2008. Test No. 4, comprehensive.
• Thursday, December 4, 2008. Test No. 5, comprehensive.
• Friday, December 12, 2008. 10:00 a.m. — 12:00 noon. Test No. 6, comprehensive.

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All information contained here is, to our best knowledge, correct, but it is merely a representation, and should not be considered to be any form of professional advice. This electronic publication should not be misconstrued as the official position of Illinois State University, or its Department of Mathematics. We are glad to provide as much information as possible here, but we kindly ask that in any decision related to matters listed here you seek additional counsel and information. Comments on this Home Page are welcome and should be sent to Dr. Krzysztof Ostaszewski  at his e-mail address: krzysio@ilstu.edu.