Torsten Trimborn

MathCCES
Department of Mathematics
RWTH Aachen University
Schinkelstr. 2
D-52062 Aachen
Germany

Room: 229 (Rogowski building, 2nd floor)
Phone: +49 (0)241 80 98 671
Email: Torsten Trimborn

Office Hours

By appointment, please send me an Email.

Research

My project deals with the derivation of kinetic financial market models out of agent-based econophysical models. The resulting kinetic models are mean field models and closely related to Mean Field Games. Furthermore, we focus on the connection between the design of the microscopic financial agents and macroscopic behaviour of the kinetic model. We hope to investigate new answers regarding the relationship between the psychological behaviour of investors and empirical observations on financial markets, known as stylized facts.

Research Interests

  • Kinetic and Mean Field Modeling
  • Mean Field Games
  • Econophysics, particularly Agent-Based Models
  • Mathematical Finance
  • Uncertainty Quantification

Projects

For students of Mathematics, CES, Physics, Economics and Computer Science I offer seminars, master or bachelor theses and paid 'HiWi projects for the research project Mean-Field Models of Financial Markets. If you are interested please send an Email.

Econophysical Financial Market Models (Thesis, Seminar or Project)
The starting point of my research are agent-based financial market models. The goal of these econophysical models is to discover connections between the microscopic agent and market design and the formation of stylized facts in financial data. Stylized facts are universal market properties, which can be observed at stock markets all over the world. One famous example are Pareto tails in income distributions and stock returns. Depending of the knowledge and interest of the participants the focus can be put on different aspects e.g.:

  • Monte Carlo Simulations, details can be found here
  • Analysis, Bifurcation Theory, details can be found here
  • Parallelization, details can be found here
  • Sensitivity Analysis using Automatic Differentiation, details can be found here

Mean-Field Models of Financial Markets (Thesis, Seminar or Project)
The application of kinetic theory to financial markets is rather new and started in the last decade. Many financial market models in economics are designed as systems of multi-agent interactions. The goal of these market models is to give explanations for the appearance of so called stylized facts. Computer simulations of econophysical models have shown that irrational behavior of financial agents might be the reason for stylized facts. Starting from microscopic agent-based models one can derive mesoscopic/kinetic models in which not the actions of the agents themselves are studied but instead the statistical probabilities of agents behaving in certain ways. These kinetic models can be studied by analyzing PDEs. Depending of the knowledge and interest of the participants the focus can be put on different aspects e.g.:

  • Monte Carlo Simulations
  • Modeling of Financial Agents
  • Kinetic Models

Detailed information on this project can be found here.

More open projects can be found here.

About me

After my Master degree in Mathematics, I started as a PhD student in the group of Prof. Frank. Furthermore, I am an associated fellow at the Aachen Institute of Advanced Study in Computational Engineering Science (AICES).

  • since 10/2013 PhD student at MathCCES, RWTH Aachen University
  • 09/2013 M.Sc. in Mathematics at RWTH Aachen University
  • 08/2011-01/2012 Erasmus exchange student at Lund University, Sweden
  • 03/2011 B.Sc. in Mathematics at RWTH Aachen University

Teaching

Sensitivity Analysis of an Econophysical Model using Stochastic Collocation,
Emma Pabich, Till Beemelmanns, Simon Cramer, Projektarbeit CES, 2015
Agent-based economic market models, Tom Lukas Witter, Chun-Kan Gary Chow, RWTH Aachen, UROP International 2015
Mathematische Grundlagen V (CES), WS 2015/16
CAMMP - Computational and Mathematical Modeling Program, SS 2015
Agent-based economic market models, Allison Roderick, The University of Texas at Dallas, UROP International 2015
Mathematische Grundlagen IV (CES), SS 2015
An econophysical financial market model, Paul Luckner, Physics Bachelor, 2015
Mathematische Grundlagen III (CES), WS 2014/15
Mathematische Grundlagen II (CES), SS 2014
Implementation of a Finite Difference Solver for the Fokker-Planck equation, Hamza Mesbahi, Internship, SS 2014
Exploratory Teaching Space project: problem-oriented math teaching
CAMMP - Computational and Mathematical Modeling Program, SS 2014
CAMMP - Computational and Mathematical Modeling Program, WS 2013/14

Last modified: 2016/02/25 11:08