Mathematical Finance :
The aim of Mathematical Finance is to give accurate mathematical models
for real world financial markets. The methods in Mathematical Finance
are mainly based on methods from Probability Theory, Statistics and
Analysis. However more and more methods from other parts of mathematics
are introduced in Mathematical Finance. I work on applications of Malliavin Calculus techniques as well as
Anticipative Calculus and Insider Trading, on general equilibrium
theory for financial markets and information structures.
Game Theory :
The aim of Game Theory is to give accurate mathematical models for
conflicts. Such conflicts can arise in any situation you could think of
( like Economics, Politics, Sociology, Animal Behavior etc ). I study game theoretic questions
within the context of Mathematical Finance and Mathematical Economics
as well as in the context of general behavioral
game theory.
Analysis on singular Spaces : A
singular space is a space which is not smooth ( as a smooth manifold
for example ) but admits singularities ( like corners, edges,
self-intersections etc. ) The Analysis for such spaces is not as well
developed as the analysis for Euclidean space or manifolds. I study
questions like which structures from Differential Geometry can be
generalized to these spaces or how Brownian motion should be defined.
Monetary Policy : I
work on game theoretic models ( stochastic continuous time ) which
model the conflict between the central bank and the public sector with
particular focus on the information assymetry.
