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Mathematics 483, Mathematical Models in Finance and Investments, Fall 2020

Illinois State University Mathematics Department

Instructors

Dr. Krzysztof Ostaszewski, FSA, CERA, FSAS, CFA, MAAA, Actuarial Program Director
Office: Stevenson Hall room 313G. Office telephone: 309-438-7226, office fax: 309-438-5866. E-mail: krzysio@ilstu.edu

Mr. Robert Gomez, FSA, Actuary, State Farm Insurance Companies. E-mail: robert.gomez.psa0@statefarm.com

Classes Meet

Tuesdays and Thursdays 6:00-7:50 p.m. (with a ten minute break), online, via Zoom. Information about Zoom access has been sent to all students enrolled in the class. If you experience any trouble accessing the class using Zoom, call Dr. Ostaszewski immediately.

Office Hours

Office hours will be held Tuesdays 2:30 p.m.– 3:50 p.m., by Dr. Krzysztof Ostaszewski, through Zoom at: https://illinoisstate.zoom.us/my/krzysio. 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, 11th edition, McGraw-Hill, 2018, ISBN 978-1259277177.
• John Hull, Options, Futures and Other Derivatives, 10th Edition, Pearson, 2017, ISBN: 978-0134472089.

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 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 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.  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 Reggienet 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.

All tests in the class will be either take-home tests or be given online. Note that use of a webcam by each student may be required for tests in this class that will be given online. All test work must be submitted in Reggienet.

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 2020 semester is given at: https://registrar.illinoisstate.edu/downloads/Fall%202020%20Withdrawal%20Dates.pdf

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 18, 2020.  Overview of assets, liabilities and capital of financial intermediaries and regulatory supervision of them.
  • Thursday, August 20, 2020. Financial Assets. Review of derivatives securities. Role of derivative securities in financial intermediaries.
  • Tuesday, August 25, 2020. Brownian Motion and Black-Scholes Model. Black-Scholes-Equation.
  • Thursday, August 27, 2020. Ito Processes, Ito’s Lemma.Valuation of derivative securities.
  • Tuesday, September 1, 2020. Interest rates derivatives and their modeling and relevance in management of an insurance firm.
  • Thursday, September 3, 2020. Interest Rate Risk Management. Class taught by Mr. Robert Gomez.
  • Tuesday, September 8, 2020. Interest Rate Risk Management. Class taught by Mr. Robert Gomez.
  • Thursday, September 10, 2020. Interest Rate Risk Management. Class taught by Mr. Robert Gomez.
  • Tuesday, September 15, 2020. Interest Rate Risk Management. Class taught by Mr. Robert Gomez.
  • Thursday, September 17, 2020. Stochastic processes modeling interest rates.
  • Tuesday, September 22, 2020. Stochastic processes modeling interest rates. No-Arbitrage Pricing Theory.
  • Thursday, September 24, 2020. Test No. 1, on the material covered through September 22, 2020 (but not No-Arbitrage Pricing Theory).
  • Tuesday, September 29, 2020. Special presentation by Mr. Isaac Nyarko, FSA, of Allianz Life, about hedging of variable annuities.
  • Thursday, October 1, 2020. No-Arbitrage Pricing Theory.
  • Tuesday, October 6, 2020. No-Arbitrage Pricing Theory.
  • Thursday, October 8, 2020, Insurance securitization. Derivative securities embedded in insurance contracts.
  • Tuesday, October 13, 2020. Introduction to Enterprise Risk Management. Coherent Risk Measures.
  • Thursday, October 15, 2020. Test No. 2, on the material covered through October 13, 2020.
  • Tuesday, October 20, 2020. Value at Risk. Conditional tail expectation.
  • Thursday, October 22, 2020. Theory of capital for insurance firms: Expected Policyholder Deficit.
  • Tuesday, October 27, 2020. Shortfall Constraints and risk management for pension plans.
  • Thursday, October 29. 2020. Risk-Based Capital in the U.S. insurance regulation. Overview of Solvency II and Swiss Solvency Test.
  • Tuesday, November 3, 2020. Election Day. Holiday.
  • Thursday, November 5, 2020. Test No. 3, on the material covered through November 3, 2020.
  • Tuesday, November 10, 2020. Equilibrium Pricing. Class taught by Mr. Robert Gomez.
  • Thursday, November 12, 2020. Equilibrium Pricing. Class taught by Mr. Robert Gomez.
  • Tuesday, November 17, 2020. Equilibrium Pricing. Class taught by Mr. Robert Gomez.
  • Thursday, November 19, 2020. Equilibrium Pricing. Class taught by Mr. Robert Gomez.
  • Tuesday, December 1, 2020. Test No. 4, comprehensive. Any of the last three tests can count as your final examination.
  • Thursday, December 3, 2020. Test No. 5, comprehensive. Any of the last three tests can count as your final examination.
  • Tuesday, December 8, 2020, 5:30 p.m. — 7:30 p.m.. Test No. 6, comprehensive. Any of the last three tests can count as your final examination.

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.

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