**Instructor:**Richard Sowers**Office:**227B Illini Hall**Phone:**(217) 333-6246**email:**r-sowers@math.uiuc.edu**Home page:**`https://faculty.math.illinois.edu/~r-sowers`

(this syllabus can be found there)**Office Hours:**MWF 12-1 and by appointment**Class meets:**MWF 2-2:50 P.M. in 155 Altgeld Hall

**Outline:** This is an undergraduate course on
some mathematical aspects of finance.

- We will start by understanding some very basic models (binomial models) involving financial derivatives (e.g., options). We will go very slowly with this since it illustrates a central idea: arbitrage pricing. We will come back to this problem later, passing to a continuum limit and getting the celebrated Black-Scholes formula.
- We will then consider mean-variance analysis and the Capital Asset Pricing Model (CAPM). Once again, we will build up a theory from very simple examples. Roughly, the question we will investigate is how one should invest. This will involve a bit of probability and a bit of linear programming. We will take this as slowly as needed.
- To end the semester, we will return to options pricing and heuristically pass to a limit and get a continuum model. In doing so, we will discuss a framework for considering exotic options.
- If there is any time left, we will consider subjects which are suggested by the class.

The tone of the class will, as much as possible, be exploratory; I would like to forego the standard Socratic method for a more conversational framework. Ideally, I would like to present the basic ideas of some material and then have students present some material which can expand upon the basic ideas. Although it would help if you have had Math 361, it is not formally a prerequisite. In other words, although I would like mathematical maturity, I will settle for mathematical adolescence. This means that the students backgrounds will wildly vary and that we will need to proceed slowly (in contrast to the standard courses which need to proceed at a fixed pace due to curricular considerations); both sophomores, juniors, and seniors will hopefully find the material accessible.

**Grading policy:** There will be three exams, final,
and either some homeworks or some class presentations.
The relative weights will be:

Final: | 150 pts (30% of grade) |

Hourly Exam 1: | 100 pts (20% of grade) |

Hourly Exam 2: | 100 pts (20% of grade) |

Hourly Exam 3: | 100 pts (20% of grade) |

Homework/Presentation: | 50 pts (10% of grade) |

Total: | 500 pts (100% of grade) |

Department of Mathematics

University of Illinois at Urbana-Champaign

1409 W Green St.

Urbana, IL 61801

r-sowers@math.uiuc.edu

(217) 333-6246