# Jerusalem Mathematics Colloquium

Thursday, 3rd March 2005, 4:00 pm

Mathematics Building, Lecture Hall 2

##

Professor Hans Foellmer

(Humboldt University)

"Stochastic analysis of financial options"

** Abstract: **

The price fluctuation of liquid financial assets is usually modeled as
a stochastic process
which satisfies some form of the "efficient markets hypothesis". Such
assumptions
can be made precise in terms of martingale measures. We discuss the
role of these martingale measures
in analyzing financial derivatives such as options, viewed as
non-linear functionals of the underlying stochastic process.

Uniqueness
of the martingale measure
provides the mathematical key to a perfect "hedge" of a financial
derivative by means of a dynamic trading strategy in the underlying
assets, and in particular to pricing formulas of Black-Scholes type.
But for realistic models the martingale measure is no longer unique,
and intrinsic risks appear on the level of derivatives. We discuss
various mathematical approaches to the problem of pricing and hedging
in such a setting.

Light refreshments will be served outside the lecture hall at 3:30.

This is the first of the
Landau Lectures
2004/2005.

List of talks, 2004-05

List of talks, 2003-04

List of talks, 2002-03

List of talks, 2001-02

List of talks, 2000-01

List of talks, 1998-99

List of talks, 1997-98