Philip H. Dybvig
Washington University in Saint Louis
Welcome to Mathematical Finance! We will cover some interesting mathematical tools that are very useful in practice, with a focus on applications to investments.
Slides I will use the whiteboard in the classroom. This is a good format for technical material. However, I have also developed a set of slides for your use as supplemental material.
Lecture 1: Decision theory and static choice problems
Lecture 2: Dynamic programming
Lecture 3: Multiple assets, hedging state variables, and pricing models
Lecture 4: FTAP, valuation, and the one-shot approach
Homeworks Here are homeworks you can work to help to learn the material. Although they will not be graded, I urge you to work the homeworks before the TA session when they will be discussed.
Extra Readings I suggest the following book chapter for background readings on single-period models:
Download Dybvig, Philip H. and Stephen A. Ross (2003), Arbitrage, State Prices, and Portfolio Theory, in George Constantinides and René Stulz, ed., Handbook of the Economics of Finance, volume 1b, North-Holland.
There is no textbook for the class, and the class is designed to be self-contained. If you want a textbook for an alternative exposition and coverage of more topics, I recommend the following book:
Back, Kerry, 2017, Asset Pricing and Portfolio Choice Theory, second edition, Oxford University Press.
Kerry is a serious scholar and my co-author. He was formerly at Washington University, but he has moved to Rice University.