Mathematics 483, Mathematical Models in Finance and Investments, Fall 2011

Illinois State University Mathematics Department

Instructors

Classes Meet

Tuesdays and Thursdays 7:00-8:50 p.m. (with a ten minute break), in Stevenson Hall, room 310.

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

The following textbooks are suggested, but not required:

• Financial Risk Management for Pension Plans by Leslaw Gajek and Krzysztof Ostaszewski, Elsevier Science, 2004. This book is on reserve at the Milner Library at Illinois State University and on reserve at the library of the Department of Mathematics.

• Financial Economics, edited by Harry Panjer, published in 1998 by the Actuarial Foundation. This book is on reserve at the Milner Library at Illinois State University.

There will also be study notes provided online by Dr. Krzysztof Ostaszewski (you must use the ISU ULID with your password to access them, and you are only granted access if you are registered in this class). We will also use study notes and problems from past actuarial examinations on investments, as well as other readings on topics of those past exam examinations. Links to those readings will be posted at the bottom of this syllabus, after the schedule of classes.

Objective

The objective of this class is to help you learn about mathematical models in finance and investments, as utilized in the management as well as financial supervision of insurance enterprises and other financial intermediaries.

Grading

There will be a total of five 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 10% extra credit for the best of the remaining tests. The grading scale for will be as follows: 90% or better — A, 80% to 90% — B, 70% to 80% — C, 60% to 70% — D, below 60% — F. Links to past professional actuarial examinations are provided below, and those professional examinations should serve as a guidance of what kind of material students can expect on the tests. However, the tests in this class will be quantitative only, no essay questions will be given. Even though questions will be quantitative only, students are encouraged to explain their work thoroughly. Students will also have an opportunity to earn extra creditby making presentations in class on the readings given in the syllabus(see the bottom of this web site) and past advanced actuarial examinations on the topics of this class (also see below). Those presentations must be set well in advance with Dr. Ostaszewski, and presentations scheduled at the last minuted before the end of the semester may be denied.

Important dates

Illinois State University withdrawal information for the Fall 2011 semester is given at this web site: http://www.registrar.ilstu.edu/registration/withdrawal/fall.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 University. 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 23, 2011. Financial Assets. Class taught by Mr. Dale Hall. There are some additional files for the Financial Assets class from Dale:
  • Financial assets and how they are traded (Powerpoint file)
  • Trading on margin (Powerpoint file)
• Thursday, August 25, 2011. Derivative Securities. Section 7.3 in first texbook. Class taught by Mr. Dale Hall.
• Tuesday, August 30, 2011. Derivative Securities. Section 7.3 in first texbook. Class taught by Mr. Dale Hall.
• Thursday, September 1, 2011. Derivative Securities. Section 7.3 in first texbook. Class taught by Mr. Dale Hall. There are some additional files for the Derivative Securities classes from Dale:
  • Derivative Securities (Powerpoint file)
  • Calculations of prices of forwards and options (Excel file)
  • Arbitrage examples (Word file).
• Tuesday, September 6, 2011. Interest Rate Risk and Immunization. Chapter 9 in first textbook.
• Thursday, September 8, 2011. Interest Rate Risk and Immunization. Chapter 9 in first textbook.
• Tuesday, September 13, 2011. Special presentation by Mr. Richard Bill, FCAS, on catastrophe insurance, in STV 401.
• Thursday, September 15, 2011. Special presentation by Dr. Wei Hao, FSA, on asset-liability management in practice, in STV 401.
• Tuesday, September 20, 2011. Insurance Securitization.Introduction to Enterprise Risk Management.
  • Additional reading: Presentation of Dr. Kevin Ahlgrim, ASA, at the 2006 ISU Actuarial Program Research Event.
  • Another reading on ERM.
• Thursday, September 22, 2011. Test No. 1, on the material covered through September 20, 2011.
• Tuesday, September 27, 2011. No-Arbitrage Pricing Theory. Sections 7.1.4, 7.1.5, 7.2 in first textbook.
• Thursday, September 29, 2011. No-Arbitrage Pricing Theory. Sections 7.1.4, 7.1.5, 7.2 in first textbook.
• Tuesday, October 4. 2011. No-Arbitrage Pricing Theory. Sections 7.1.4, 7.1.5, 7.2 in first textbook.
• Thursday, October 6, 2011. Value at Risk. Also, another version of Value at Risk notes is here.
• Tuesday, October 11, 2011. Test No. 2, on the material covered through October 4, 2011.
• Thursday, October 13, 2011. Shortfall Constraints. Sections 10.1.1, 10.1.3 in first textbook.
• Tuesday, October 18, 2011. Equilibrium Pricing. Sections 7.1.2, 7.1.3 in first textbook. Class taught by Mr. Dale Hall.
• Thursday, October 20, 2011. Equilibrium Pricing. Sections 7.1.2, 7.1.3 in first textbook. Class taught by Mr. Dale Hall.
• Tuesday, October 25, 2011. Equilibrium Pricing. Sections 7.1.2, 7.1.3 in first textbook. Class taught by Mr. Dale Hall. There are some additional files for the Equilibrium Pricing classes from Dale:
  • Equilibrium Pricing (Powerpoint file)
  • Utility functions (Excel file)
• Thursday, October 27, 2011. Theory of capital for insurance firms:
  • Expected Policyholder Deficit.
  • Coherent Risk Measures.
  • Risk-Based Capital in the U.S. insurance regulation.
• Tuesday, November 1. 2011. Theory of capital for insurance firms:
  • Myers & Read on Capital Allocation for Insurance Companies.
  • Cummins on Capital Allocation for Insurance Companies.
  • Goldfarb on Risk-Adjusted Performance Measurement for Insurance Companies.
• Thursday, November 3. 2011. Solvency II and Swiss Solvency Test.
  • More files on these topics
    • Solvency II vs. Swiss Solvency Test
    • Swiss Solvency Test White Paper
    • Swiss Solvency Template
    • Swiss Solvency Test Reading 1
• Tuesday, November 8, 2011. Options and Other Derivatives. Class taught by Mr. Dale Hall.
• Thursday, November 10, 2011. Options and Other Derivatives. Class taught by Mr. Dale Hall.
• Tuesday, November 15, 2011. Options and Other Derivatives. Class taught by Mr. Dale Hall.
• Thursday, November 17, 2011. Options and Other Derivatives. Class taught by Mr. Dale Hall.
• Tuesday, November 29, 2011 . Role of Interest Rate Derivative Securities.
• Thursday, December 1, 2011. Additional exercises for preparation for the remaining class tests. Risk-Based Capital Exercises.
• Tuesday, December 5, 2011. Test No. 3, comprehensive.
• Thursday, December 8, 2011. Test No. 4, comprehensive.
• Tuesday, December 13, 2011, 5:30-7:30 p.m. in STV 310 (regular room). Test No. 5, comprehensive.

Past actuarial examinations on topics of this class include Society of Actuaries exams APM/APMV, AFE, FETE, Course 6 (2000-2006), and Course 8V (2000-2006), and Casualty Actuarial Society exams 7 and 9, as well as exam 8 (2000-2010). You may want to consult these exams posted at these societies’ web sites for practice problems, and another sources of possible extra credit presentations in class.

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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.