285K (Fall 2008) – Introduction to Mathematical Finance

Instructor: Roberto Schonmann

Time: MW 9 to 10:50 (actually we may do only hour and a half or so each time, but we have flexibility, given that we have the room reserved for the two hours).

Place: MS 6221

We will use the book by R. Elliott and P.E. Kopp “Mathematics of Financial Markets” (2^nd edition, Springer 2005).

Half of the material will be about markets that operate in discrete time. The main goal will be to cover the two fundamental theorems of mathematical finance, in this setting: 1) Absence of arbitrage is equivalent to the existence of an equivalent martingale measure.

2) Completeness of the market is equivalent to the uniqueness of that equivalent martingale measure.

The second half of the course will be an introduction to hedging and pricing derivative securities in continuous time models (starting with Black-Scholes, and hoping to have time for interest rate market models).

Students will be supposed to have a solid understanding of basic graduate probability in a discrete time setting (e.g., from 275AB). A solid understanding of Brownian motion (e.g., from 275C) and possibly of stochastic calculus (e.g., from 275D) is welcome, but not assumed. For this reason, I plan to summarize the basic facts about Brownian motion and stochastic calculus when we start the second half of the course.

This course will be quite different from the 275D that I taught in the Fall 2007, and students from that course are welcome in the current one.