Modern probability theory has many facets. On one hand, as through all its history, it deals with applied problems coming from different areas of human activity, like physics, biology, informatics, economy, banking or insurance. On the other hand, it is a flourishing branch of mathematics, with many connections to its other sub-fields. The main strength of the Probability Theory and Mathematical Finance group at University of Vienna is in balancing those different facets, in contributing to both fundamental research and applied questions.
In the field of mathematical finance, the group combines and develops the ideas coming from stochastic and functional analysis, and the theory of optimal transportation to obtain new insights on the fundamental questions of portfolio optimization, and pricing and hedging of financial instruments, basing on the no-arbitrage principle.
The probability theory part of the group focuses of on various properties of disordered systems, inspired by questions coming mainly from physics, in particular statistical mechanics. Its main activities lie in the studies of processes in random environment and in percolation theory.