Mathematics 483, Mathematical Models in Finance and Investments, Fall 2019

Illinois State University Mathematics Department

Instructors

Classes Meet

Tuesdays and Thursdays 6:00-7:50 p.m. (with a ten minute break), in Stevenson Hall, room 325.

Office Hours

Office hours will be held Tuesdays 2:30 p.m.– 3:50 p.m., in Stevenson Hall room 313G, by Dr. Krzysztof Ostaszewski. Please ask for an appointment at other times. Appointments with Dr. Krzysztof Ostaszewski should be scheduled at: http://smartURL.it/appointment.

Textbooks

There will be study notes, practice exams, and optional readings for presentation in class provided by Dr. Krzysztof Ostaszewski  in Reggienet.
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.
• Zvi Bodie, Alex Kane, and Alan J. Marcus, Investments, 10th edition, McGraw-Hill, 2014, ISBN 9780077861674.
• John Hull, Options, Futures and Other Derivatives, 9th Edition, Pearson, 2016, ISBN: 9780133456318.

Students can earn extra credit for making presentations in class and for discussions in class on advanced readings, mostly related to the Society of Actuaries Quantitative Finance and Investment Track Fellowship exams, and to the Casualty Actuarial Society Course 9 Examination on Financial Risk and Rate of Return. Some potential readings for presentation are provided in the class online platform, in Reggienet.

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 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 10% extra credit for the best two (each) 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 suggested in Reggienet or other readings from Fellowship level examninations of the Society of Actuaries or the Casualty Actuarial Society. 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 2019 semester is given at this web site: http://www.registrar.ilstu.edu/registration/withdrawal/fall.shtml.

Accommodation

Any student needing to arrange a reasonable accommodation for a documented disability and/or medical/mental health condition should contact Student Access and Accommodation Service at 350 Fell Hall, (309) 438-5853, or visit the website at StudentAccess.IllinoisState.edu.

No recording of this class is allowed

Students may not photograph or use audio or video devices to record classroom lectures or discussions or visual materials that accompany them (e.g., lecture slides, whiteboard notes/equations). Students with disabilities who need to record classroom lectures or discussions must contact Student Access and Accommodation Services to register, request and be approved for an accommodation. Students who violate this policy may be subject to both legal sanctions for violations of copyright law and disciplinary action under the University’s Code of Student Conduct.

Schedule of classes

• Tuesday, August 20, 2019. Overview of assets, liabilities and capital of financial intermediaries and regulatory supervision of them.
• Thursday, August 22, 2019. Financial Assets. Review of derivatives securities. Role of derivative securities in financial intermediaries.
• Tuesday, August 27, 2019. Brownian Motion and Black-Scholes Model. Black-Scholes-Equation.
• Thursday, August 29, 2019. Ito Processes, Ito’s Lemma.Valuation of derivative securities.
• Tuesday, September 3, 2019. Interest rates derivatives and their modeling and relevance in management of an insurance firm.
• Thursday, September 5, 2019. Interest Rate Risk Management. Chapter 9 in first textbook. Class taught by Dr. Wei Hao.
• Tuesday, September 10, 2019. Interest Rate Risk Management. Chapter 9 in first textbook. Class taught by Dr. Wei Hao.
• Thusday, September 12, 2019. Interest Rate Risk Management. Chapter 9 in first textbook. Class taught by Dr. Wei Hao.
• Tuesday, September 17, 2019. Stochastic processes modeling interest rates.
• Thursday, September 19, 2019. Stochastic processes modeling interest rates.
• Tuesday, September 24, 2019. No-Arbitrage Pricing Theory.
• Thursday, September 26, 2019. No-Arbitrage Pricing Theory.
• Tuesday, October 1, 2019. No-Arbitrage Pricing Theory.
• Thursday, October 3, 2019. No-Arbitrage Pricing Theory.
• Tuesday, October 8, 2019. Test No. 1, on the material covered through October 3, 2019.
• Thursday, October 10, 2019,  Insurance securitization. Derivative securities embedded in insurance contracts.
• Tuesday, October 15, 2019. Introduction to Enterprise Risk Management. Coherent Risk Measures.
• Thursday, October 17, 2019. Value at Risk. Conditional tail expectation.
• Tuesday, October 22, 2019. Theory of capital for insurance firms: Expected Policyholder Deficit.
• Thursday, October 24, 2019. Risk-Based Capital in the U.S. insurance regulation. Overview of Solvency II and Swiss Solvency Test.
• Tuesday, October 29, 2019. Test No. 2, on the material covered through October 24, 2019.
• Thursday, October 31. 2019. Equilibrium Pricing. Class taught by Dr. Wei Hao.
• Tuesday, November 5, 2019. Equilibrium Pricing. Class taught by Dr. Wei Hao. 
• Thursday, November 7, 2019. Equilibrium Pricing. Class taught by Dr. Wei Hao.
• Tuesday, November 12, 2019. Equilibrium Pricing. Class taught by Dr. Wei Hao.
• Thursday, November 14, 2019. Test No. 3, on the material covered through November 12, 2019.
• Tuesday, November 19, 2019. Special presentation on asset-liability management in practice at State Farm Insurance by Dr. Wei Hao, FSA, CFA, MAAA. This class will be also be an event of the Actuarial Program and will be held in Stevenson Hall room 101 (note the unusual location).
• Thursday, November 21, 2019. Shortfall Constraints and risk management for pension plans.
• Tuesday, December 3, 2019. Test No. 4, comprehensive.
• Thursday, December 5, 2019. Test No. 5, comprehensive.
• Tuesday, December 10, 2019, 5:30 p.m. (note the unusual time). 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.