PROBABILISTIC ASPECTS OF FINANCIAL RISK

HANS FOLLMER
Humboldt-Universitat zu Berlin

Wednesday, 20 March 2002, at 16:30, Friend Center 101

We discuss some probabilistic problems which arise as we move beyond the Black-Scholes paradigm of a perfect hedge. If such a perfect hedge exists, we do not need a discussion of preferences in the face of risk and uncertainty. In an incomplete model, such preferences have to be made explicit. In particular, this will involve quantitative measures of risk. We discuss representation theorems for measures of risk beyond Value at Risk such as the coherent risk measures introduced by Artzner, Delbaen, Eber and Heath. This is related to the Savage-Huber-Gilboa-Schmeidler representation of robust preferences on a space of financial positions. We also discuss the structure of hedging strategies which are efficient in terms of cost and shortfall risk.

RATES FOR EULER SCHEMES FOR EQUATIONS DRIVEN BY LEVY PROCESSES

JEAN JACOD
Universite de Paris VI
Thursday, 21 March 2002, at 9:30, Friend Center 101

RIGOROUS RESULTS FOR THE NK MODEL

VLADA LIMIC
Cornell University

Thursday, 21 March 2002, at 11:15, Friend Center 101

In 1987, Stuart Kauffman and Simon Levin introduced the NK model motivated by the problem of the evolution of DNA sequences. To each sequence of 0-1 bits of length N, they assigned a fitness as a sum of (random) quantities that depend only on bits observed in a sliding window of length K.

The random map obtained in this way is called the fitness landscape. When 1

ADDITIVE LEVY PROCESSES

> DAVAR KHOSHNEVISAN
University of Utah

Friday, 22 March 2002, at 9:30, Friend Center 101

CENSORED STABLE PROCESSES

ZHEN-QING CHEN
University of Washington

Friday, 22 March 2002, at 11:15, Friend Center 101

A censored alpha-stable process Y in an open set D is a process that is obtained from a symmetric alpha-stable Levy process by prohibiting that it makes jumps outside D. We will address the question of whether the process Y will approach the boundary of D in a finite time, as well as the potential theory for transient censored stable processes, including Harnack and boundary Harnack principles, sharp estimates for Green functions and Martin kernels, identification of Martin boundary. We will also discuss processes obtained from Y by jump intensity perturbations.

FILTRATIONS IN THE LIGHT OF CLASSIFICATION THEORY

BORIS TSIRELSON
Tel-Aviv University

Saturday, 23 March 2002, at 9:30, Friend Center 101

Brownian motions of different dimensions generate non-isomorphic filtrations. Corresponding invariants are well understood. They inspire hope of an exhaustive classification of all filtrations. However, the hope is undermined by unexpected new invariants: splitting multiplicity, coziness.

Classification theory, dealing with orbit equivalence relations on Polish G-spaces, tells us that some objects are classifiable and some are not. Known examples belong to various branches of mathematics.

The classification theory can be applied to filtrations (filtered probability spaces). I report first results in this direction. A topological zero-one law states that for every property of filtrations, either the property holds for almost all filtrations, or its negation does.