Mathematics 483, Mathematical Models in Finance and Investments, Fall 2024

Illinois State University – Mathematics Department
All class materials are available on Canvas

Instructors

Classes Meet

This is a hybrid class. In person meetiings will be Tuesdays and Thursdays 6:00-7:50 p.m. (with a ten minute break), in Stevenson Hall room 310, while  online classes will be held via Zoom, or in an asynchronous manner, if necessary. If you experience any trouble accessing the class using Zoom, call Dr. Ostaszewski immediately at his office telephone number or his cell telephone number: 309-287-1711.

Office Hours

Office hours will be held by Dr. Krzysztof Ostaszewski by appointment, in person in his office, or through Zoom at: https://illinoisstate.zoom.us/my/krzysio. Appointments with Dr. Krzysztof Ostaszewski should be scheduled at: http://smartURL.it/appointment. E-mail or call Dr. Krzysztof Ostaszewski if you need help quickly.

Textbooks

There will be study notes, practice exams, and optional readings for presentation in class provided by Dr. Krzysztof Ostaszewski  in Canvas. 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. This book will also be available through the Milner library in an online form at: https://i-share-isu.primo.exlibrisgroup.com/permalink/01CARLI_ISU/179j7oq/alma9921309114505845.
• 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, 11th edition, McGraw-Hill, 2018, ISBN 978-1259277177.
• John Hull, Options, Futures and Other Derivatives, 10th Edition, Pearson, 2017, ISBN: 978-0134472089.

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 many opportunities for testing and only the best three scores will affect the class grade (but with the opportunity for extra credit for two more tests), 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 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.  Past professional examinations can also serve as a guidance of what kind of material students can expect on the tests. You can find past Society of Actuaries examinations at: http://smartURL.it/pastSOAexams, and past Casualty Actuarial Society examinations at: http://smartURL.it/pastCASexams. 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 credit by making presentations in class on the readings suggested in Canvas or other readings from Fellowship level examinations 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.

Class attendance

While this class does not have a strict formal attendance requirement, students who actively participate in class, and make a significant contribution may be granted extra credit. You are expected to attend classes and be involved in the learning process. If you must miss class due to an extended illness (3 or more consecutive class days) or bereavement, the Student Health Services and the Dean of Students Office can help. Please note this university policy: Excused Student Absences Due to Communicable Disease.

Important dates

Illinois State University withdrawal information for the Fall 2024 semester is given at the University Registrar site.

Student Access and Accommodation Services

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, 2024.  Overview of assets, liabilities and capital of financial intermediaries and regulatory supervision of them.
• Thursday, August 22, 2024. Financial Assets. Review of derivatives securities. Role of derivative securities in financial intermediaries.
• Tuesday, August 27, 2024. Interest rates derivatives. Insurance securitization. Derivative securities embedded in insurance contracts.
• Thursday, August 29, 2024. Ito Processes, Ito’s Lemma.Valuation of derivative securities.
• Tuesday, September3, 2024. Brownian Motion and Black-Scholes Model. Black-Scholes-Equation.
• Thursday, September 5, 2024. Stochastic processes modeling interest rates.
• Tuesday, September 10, 2024. No-Arbitrage Pricing Theory.
• Thursday, September 12, 2024.  No-Arbitrage Pricing Theory.
• Tuesday, September 17, 2024. This class will be replaced by the Meet the Firms event.
• Thursday, September 19, 2024. Special presentation by Ms. Minchong Mao, FCAS, ASA, Managing Director, Reinsurance Solutions at Aon, on modeling of catastrophe risk.
• Tuesday, September 24, 2024. Special presentation by Mr. Isaac Nyarko, FSA, on hedging of deferred annuities contracts.
• Thursday, September 26, 2024. Test No. 1, on the material covered through September 12, 2024.
• Tuesday, October 1, 2024: Interest Rate Risk Management. Class taught by Mr. Robert Gomez.
• Thursday, October 3, 2024. Interest Rate Risk Management. Class taught by Mr. Robert Gomez.
• Tuesday, October 8, 2024: Interest Rate Risk Management. Class taught by Mr. Robert Gomez.
• Thursday, October 10, 2024. Interest Rate Risk Management. Class taught by Mr. Robert Gomez.
• Tuesday, October 15, 2024. Equilibrium Pricing. Class taught by Mr. Robert Gomez.
• Thursday, October 17, 2024. Equilibrium Pricing. Class taught by Mr. Robert Gomez.
• Tuesday, October 22, 2024. Equilibrium Pricing. Class taught by Mr. Robert Gomez.
• Thursday, October 24, 2024. Equilibrium Pricing. Class taught by Mr. Robert Gomez.
• Tuesday, October 29, 2024. Test No. 2, on the material covered through October 24, 2024.
• Thursday, October 31, 2024. Enterprise Risk Management. Coherent Risk Measures.
• Tuesday, November 5, 2024. Theory of capital for insurance firms: Expected Policyholder Deficit.
• Thursday, November 7, 2024. Value at Risk. Conditional tail expectation.
• Tuesday, November 12, 2024.  Risk-Based Capital in the U.S. insurance regulation.
• Thursday, November 14, 2024. Shortfall Constraints and risk management for pension plans.
• Tuesday, November 19, 2024. Overview of Solvency II and Swiss Solvency Test.
• Thursday, November 21, 2024. Comparison and equivalence of risk measures used for capital regulation.
• Tuesday, December 3, 2024. Test No. 3, comprehensive. Any of the last three tests can count as your final examination.
• Thursday, December 5, 2024. Test No. 4, comprehensive. Any of the last three tests can count as your final examination.
• Tuesday, December 10, 2024, 4:30 p.m. – 7:10 p.m. (note the unusual time). Test No. 5, comprehensive. Any of the last three tests can count as your final examination.

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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.