3 citations · 7 across the 14 of their papers we have counts for
15 papers
Continuous limits of residual neural networks in case of large input data
M. Herty, A. Thuenen, T. Trimborn +1
Residual deep neural networks (ResNets) are mathematically described as interacting particle systems. In the case of infinitely many layers the ResNet leads to a system of coupled…
Mean-field control variate methods for kinetic equations with uncertainties and applications to socio-economic sciences
Lorenzo Pareschi, Torsten Trimborn, Mattia Zanella
In this paper, we extend a recently introduced multi-fidelity control variate for the uncertainty quantification of the Boltzmann equation to the case of kinetic models arising in…
Simplified ResNet approach for data driven prediction of microstructure-fatigue relationship
Christian Gebhardt, Torsten Trimborn, Felix Weber +3
The heterogeneous microstructure in metallic components results in locally varying fatigue strength. Metal fatigue strongly depends on size and shape of non-metallic inclusions and…
Novel Insights in the Levy-Levy-Solomon Agent-Based Economic Market Model
Maximilian Beikirch, Torsten Trimborn
The Levy-Levy-Solomon model (A microscopic model of the stock market: cycles, booms, and crashes, Economic Letters 45 (1))is one of the most influential agent-based economic market…
Mean-Field and Kinetic Descriptions of Neural Differential Equations
M. Herty, T. Trimborn, G. Visconti
Nowadays, neural networks are widely used in many applications as artificial intelligence models for learning tasks. Since typically neural networks process a very large amount of…
From Disequilibrium Markets to Equilibrium
Christian Lax, Torsten Trimborn
The modeling of financial markets as disequilibrium models by ordinary differential equations has become a popular modeling tool. One famous example of such a model is the Beja-Gol…
Stylized Facts and Agent-Based Modeling
Simon Cramer, Torsten Trimborn
The existence of stylized facts in financial data has been documented in many studies. In the past decade the modeling of financial markets by agent-based computational economic ma…
Recent developments in controlled crowd dynamics
M. K. Banda, M. Herty, T. Trimborn
We survey recent results on controlled particle systems. The control aspect introduces new challenges in the discussion of properties and suitable mean field limits. Some of the as…
Microscopic Derivation of Mean Field Game Models
Martin Frank, Michael Herty, Torsten Trimborn
Mean field game theory studies the behavior of a large number of interacting individuals in a game theoretic setting and has received a lot of attention in the past decade (Lasry a…
Robust Mathematical Formulation and Probabilistic Description of Agent-Based Computational Economic Market Models
Maximilian Beikirch, Simon Cramer, Martin Frank +3
In science and especially in economics, agent-based modeling has become a widely used modeling approach. These models are often formulated as a large system of difference equations…
Simulation of Stylized Facts in Agent-Based Computational Economic Market Models
Maximilian Beikirch, Simon Cramer, Martin Frank +3
We study the qualitative and quantitative appearance of stylized facts in several agent-based computational economic market (ABCEM) models. We perform our simulations with the SABC…
A Macroscopic Portfolio Model: From Rational Agents to Bounded Rationality
Torsten Trimborn
We introduce a microscopic model of interacting financial agents, where each agent is characterized by two portfolios; money invested in bonds and money invested in stocks. Further…
SABCEMM-A Simulator for Agent-Based Computational Economic Market Models
Torsten Trimborn, Philipp Otte, Simon Cramer +3
We introduce the simulation tool SABCEMM (Simulator for Agent-Based Computational Economic Market Models) for agent-based computational economic market (ABCEM) models. Our simulati…
Mean Field Limit of a Behavioral Financial Market Model
Torsten Trimborn, Martin Frank, Stephan Martin
In the past decade there has been a growing interest in agent-based econophysical financial market models. The goal of these models is to gain further insights into stylized facts…
Portfolio Optimization and Model Predictive Control: A Kinetic Approach
Torsten Trimborn, Lorenzo Pareschi, Martin Frank
In this paper, we introduce a large system of interacting financial agents in which each agent is faced with the decision of how to allocate his capital between a risky stock or a…