Benjamin Köhler
PhD candidate in econophysics and the statistical physics of complex systems
Guhr Group, Faculty of Physics · University of Duisburg-Essen
About
I am a physicist working on complex systems, i.e. systems whose collective behaviour emerges from the interactions of many parts, and rarely from any one of them.
My doctoral research applies the methods of statistical physics to financial markets, where correlations shift, distributions are heavy-tailed, and stationarity is the exception rather than the rule.
Before Duisburg I studied at TU Dresden, taking a Bachelor's and Master's in Physics alongside a Bachelor's in Mathematics in Business and Economics. That combination is deliberate: the questions I find most interesting sit exactly where physical modelling, stochastics and economics meet.
Earlier work took me through transport and mobility, interbank networks, and polymer physics. These are very different systems, but the same question runs through all of them: how structure and dynamics give rise to collective behaviour.
Away from the desk I take long walks in nature and seek out places of historical significance. I read philosophy and theology closely, from Plato to Machiavelli to Kierkegaard, and find the questions they ask stay with me long after the reading.
The true delight is in the finding out rather than in the knowing.
Research
My current work sits in econophysics: treating markets as non-stationary, strongly correlated multivariate systems and asking what statistical physics can say about them.
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Non-stationarity & random matrix theory
Random matrix models for multivariate distributions in systems whose correlation structure drifts over time, and the formulae needed to fit them to data.
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Extreme value analysis
Extreme value statistics for finite, multivariate and correlated systems, where the classical asymptotic results do not straightforwardly apply.
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Market microstructure
Self- and cross-response functions, non-Markovian effects, and how the empirical signature of trading has changed across crises and the rise of algorithmic trading.
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Complex networks & transport
Random walks on networks, systemic risk in interbank structures, and the route dynamics of shared mobility services.
Theses
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Efficient Reverse Stress Testing of Interbank Networks using Auto-differentiation
Reverse stress testing asks the inverse of the usual question: rather than propagating a given shock, it searches for the shocks that would push a banking system into distress. The thesis formulates this search over an interbank network and uses automatic differentiation to make it computationally tractable.
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The non-Markovian Random Walks of Ridepooling
Abstract
Ridepooling services have become an increasingly attractive mobility option in urban areas. As users issue requests for transport, ridepooling vehicles drive through the road network, continually adjusting their routes to pick up and deliver users with similar trips in shared rides. The quality of such services strongly depends on the dynamics of evolving vehicle routes, which collectively emerge from the interactions of the vehicles, requests and the dispatching algorithm. So far, theories of ridepooling services have focused on macroscopic and mean-field dynamics, neglecting the underlying microscopic route evolution. In this thesis, the structure and dynamics of these random routes in the limit of optimal service efficiency is analysed. An emerging random walk of a route that is specified not only by the current location of the vehicle, but also by the route planned ahead, is described. This process is mapped to an ordinary Markov random walk on an abstract graph whose nodes represent the shortest paths of the original street network. Thereby emerging routing patterns are identified and, with the help of event-based simulations, evaluated with respect to their implications for the ridepooling service. In addition, the calculation of an already known scaling parameter, which includes the topology of the street network, is formalised.
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The Simulation of the Synthesis of Olympic Gels through Ring-opening Polymerization
Abstract
Olympic gels are purely topologically linked networks of polymer rings. There are several methods for creating such a network. However, these methods are difficult to realize experimentally. In my thesis, the possibility of the synthesis of Olympic gels through another mechanism is analyzed and discussed. It uses the standard reaction of reversible ring-opening polymerization, which is more convenient to use in experiment. The method is implemented using the Bond Fluctuation Model (BFM) with a Metropolis algorithm. A breaking energy and an attachment energy are introduced, which model the transition probabilities from bound states to open states. The time dependence of various properties regarding formation of polycatenanes and Olympic gels are analyzed and discussed. In addition, simulation results regarding number and mass distributions of rings and chains, and therefore the ring-chain equilibrium, are compared to a set of rate equations that are solved numerically. The number of linked ring pairs per system is analyzed with the help of an algorithm using the HOMFLY-polynomial. Percolation and the size of the biggest clusters is qualitatively discussed. Formation of a gel is observed for a sample, which shows that very promising results can be achieved.
Teaching
- 2024 – present Advanced lab course Statistical Time Series Analysis: Brownian Motion, Stock Prices and Temperatures; exercise classes for Econophysics and Statistical Physics of Financial and Credit Markets; supervision of Bachelor's theses · University of Duisburg-Essen
- 2020 – 2023 Tutorials in Calculus, Linear Algebra and Mathematics for Industrial Engineering, Economics and Management; mathematics learning centre and physics teaching lab · TU Dresden
Publications
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2026
Extreme Value Analysis for Finite, Multivariate and Correlated Systems with Finance as an Example
arXiv:2603.05260 (preprint)
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2025
Multivariate distributions in non-stationary complex systems I: A random matrix model and formulae for data analysis
Journal of Statistical Mechanics: Theory and Experiment 2025(10), 103404
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2025
A new traders' game? — Empirical analysis of response functions in a historical perspective
Physica A: Statistical Mechanics and its Applications 679, 130981
Skills
- Scientific computing
- Python (NumPy, SciPy, pandas, Matplotlib, networkx, dask, ...) and Julia (Graphs.jl, DataFrames.jl, Plots.jl, ...). Numerical modelling, automated data processing and visualisation.
- Simulation
- Monte Carlo and lattice Monte Carlo methods, random walk models, agent-based and event-based simulation.
- Statistics & data analysis
- Random matrix theory, extreme value analysis, time series analysis, stochastic modelling. Terabyte-scale datasets; SQL (Oracle) and data warehouse structures.
- Complex networks
- Structural and dynamical analysis of networks, including interbank and street networks. Gephi.
- Further languages
- Fortran 95 (proficient) for scientific and numerical programming; C++ (basic), including the LeMonADE library.
- Tools & environments
- Linux (Fedora, Ubuntu, openSUSE), Git, LaTeX for papers, theses and presentations.
- Languages
- German (native), English (fluent), French (basic).
Contact
The quickest way to reach me is by email. I am happy to hear about collaborations, seminars, or questions about any of the work above.