Lecture Slides for AMSC/MATH 420: Spring 2022
Mathematical Modeling

Topic	Version	Date of Lecture
Portfolios that Contain Risky Assets
1.1. Risk and Reward	February 18	January 26
1.2. Covariance Matrices	February 18	January 28
2.1. Markowitz Portfolios	February 18	January 31
2.2. Markowitz Frontiers	February 18	February 2
2.3. Portfolio Metrics	February 18	February 4
3.1. Portfolios with Risk-Free Assets	March 15	February 7
3.2. Two-Rate Model	March 15	February 9
3.3. Metrics with Risk-Free Assets	March 15	February 11
3.4. Capital Asset Pricing Model	March 27	March 2
4.1. Long Portfolios and Their Frontiers	March 15	February 14, 16
4.2. Long Portfolios with a Safe Investment	March 15	February 16
4.3. Metrics for Long Portfolios	March 15	February 18
5.1. Limited-Leverage Portfolios	March 15	February 21
5.2. Limited-Leverage Frontiers	March 15	February 23
5.3. Limited-Leverage with Risk-Free Assets	March 15	February 25
5.4. Limited-Leverage and Return Bounds	March 15	February 28
6.1. IID Models for Single Assets	March 27	March 14
6.2. Variance Estimators and Certainty for IID Models	March 27	March 16
6.3. Central Moment Estimators for IID Models	March 27	March 18,28
7.1. Assessing Identical Distribution for IID Models	March 27	March 28
7.2. Assessing Independence for IID Models	March 27	March 30
8.1. IID Models for Markets and Portfolios	April 3	April 1,4
8.2. Law of Large Numbers for IID Models	April 3	April 4
8.3. Kelly Criterion for IID Models	April 3	April 6
9.1. Kelly Objectives for Markowitz Portfolios	April 15	April 8
9.2. Mean-Variance Estimators for Kelly Objectives	April 15	April 11
10.1. Cautious Objectives for Markowitz Portfolios	April 27	April 13
10.2. Mean-Variance Estimators for Cautious Objectives	April 27	April 15, 18
10.3. Optimizations Mean-Variance Objectives	April 27	April 20, 22, 25
10.4. Fortune's Formulas	April 15	April 27, 29

Background Material on Linear Algebra: Linear Algebra and Its Applications, Fifth Edition, by David C. Lay, Steven R. Lay, and Judi J. McDonald, Pearson, 2016.
This is the standard text for MATH 240 and 461. It (or an earlier edition) covers all the linear algebra that you need for this course.
Chapter 6 covers some of the material from the first two lectures on fitting.

Additional Material on Graphs:
Spectral Graph Theory 2nd Edition, by F. Chung, AMS 1997. See online information at: Spectral Graph Theory . Particularly useful: Chapter 1.

Background Materials on MATLAB:

• Math 241 MATLAB Materials, by Jonathan Rosenberg
  A brief introduction with examples of graphing commands.

• Getting Started with MATLAB and Simulink Student Version, by Mathworks
  This is a free on-line set of tutorials.

• Chapter 1 of Numerical Computing with MATLAB, by Cleve Moler
  This is a good general introduction to MATLAB.

• MATLAB: An Introduction with Applications, Fourth Edition, by Amos Gilat
  J. Wiley and Sons, New York, 2011
  

• An Introduction to MATLAB for Engineers, by William J. Palm III
  McGraw-Hill, New York, 2010
  

• Getting Started with MATLAB, A Quick Introduction for Scientists and Engineers, by Rudra Pratap
  Oxford University Press, New York, 2009
  (There may be some differences between the MATLAB described in this book and versions 2009b or later.)

• Essentials of MATLAB Programming, Second Edition, by Stephen J. Chapman
  Cengage Learning, Stamford CT, 2009
  (This book covers more advanced material than is needed for this course.
  This is based on MATLAB 7. I do not know if it is current with version 2009b or later.)