Dr. Torsten Trimborn

Research

My research mainly focuses on the kinetic description and modeling of interacting multi-agent systems in socio-economic applications. Mesoscopic modeling is a powerful tool to describe collective phenomena and to gain insights into the large time behavior of such multi-agent systems. My current interest is to discover novel optimal control aspects in a multi-agent environment and especially the corresponding kinetic limit. In my opinion this is one of the major challenges in the application of kinetic theory onto social-economic aspects since intelligent beings are no physical particles.

Research Interests

• Kinetic and Mean Field Modeling
• Mean Field Games
• Econophysics, particularly Agent-Based Models
• Uncertainty Quantification
• Monte Carlo Methods

Publications

• T. Trimborn, P. Otte, S. Cramer, M. Beikirch, E. Pabich, M. Frank, SABCEMM-A Simulator for Agent-Based Computational Economic Market Models, Vol. 55, Computational Economics, 2020
• T. Trimborn, L. Pareschi, M. Frank, Portfolio Optimization and Model Predictive Control: A Kinetic Approach, Vol. 24, Discrete Cont. Dyn. B, 2019
• T. Trimborn, A Macroscopic Portfolio Model: From Rational Agents to Bounded Rationality, Mathematics and Financial Economics, 2019
• T. Trimborn, M. Frank, S. Martin, Mean Field Limit of a Behavioral Financial Market Models, Vol. 505, Physica A, 2018

Preprints

• T. Trimborn, S. Gerster, G. Visconti, Uncertainty Quantification for Neural Networks, Preprint, 2020
• C. Gebhardt, T. Trimborn, F. Weber, A. Bezold, C. Broeckmann, M. Herty, Simplified ResNet approach for data driven prediction of microstructure-fatigue relationship, Preprint, 2020
• M. Beikirch, T. Trimborn, Novel Insights in the Levy-Levy-Solomon Agent-Based Economic Market Model , Preprint, 2020
• M. Herty, T. Trimborn, G. Visconti, Kinetic Theory for Residual Neural Networks, Preprint, 2020
• C. Lax, T. Trimborn, From Disequilibrium Markets to Equilibrium, Preprint, 2019
• M. Frank, M. Herty, T. Trimborn, Microscopic Derivation of Mean Field Game Models, Preprint, 2019
• M. K. Banda, M. Herty, T. Trimborn, Recent developments in controlled crowd dynamics, Preprint, 2019
• S. Cramer, T. Trimborn, Stylized Facts and Agent-Based Modeling, Preprint, 2019
• M. Beikirch, S. Cramer, M. Frank, P. Otte, E. Pabich, T. Trimborn, Robust Mathematical Formulation of Agent-Based Computational Economic Market Models, Preprint, 2019
• M. Beikirch, S. Cramer, M. Frank, P. Otte, E. Pabich, T. Trimborn, Simulation of Stylized Facts in Agent-Based Computational Economic Market Models, Preprint, 2018

Projects

• Kinetic Methods for Data Science and Deep Learning
The goal of this project is to use kinetic theory to gain novel insights into data science applications. Examples include large data clustering or inverse problems. In deep learning we are especially interested to understand the good performance of neural networks in many data science applications.


• Kinetic modeling of financial markets
Kinetic theory may help to analyze novel financial marekt models where investors are described as heterogeneous interacting agents. Such novel models help to gain insights in the creation of financial crashes. 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.


• Computational methods for agent-based financial market models
One novel and promising modeling approach of financial markets are agent-based computational financial market models, which are part of the research field econophysics. In contrast to classical models investors are modeled by heterogeneous interacting agents. These large dynamical systems are usually analyzed by means of Monte Carlo simulations. In this project we apply modern mathematical methods e.g. sparse grid collocation onto such agent-based models in order to quantify the simulation output and to understand the impact of several input parameters with respect to the appearance of stylized facts. Recently, we have introduced the simulator SABCEMM for such agent-based financial market models.