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Based on criteria of mathematical simplicity and consistency with empirical market data, a model with volatility driven by fractional noise has been constructed which provides a fairly accurate mathematical parametrization of the data.…
We investigate the full dynamics of capital allocation and wealth distribution of heterogeneous agents in a frictional economy during booms and busts using tools from mean-field games. Two groups in our models, namely the expert and the…
A new multiagent model of the stock market is formulated that contains four states in which the agents may be located. Next, the model is reformulated in the language of the functional integral containing fluctuations of prices and…
We combine geometric data analysis and stochastic modeling to describe the collective dynamics of complex systems. As an example we apply this approach to financial data and focus on the non-stationarity of the market correlation structure.…
We present a detailed study of the statistical properties of an Agent Based Model and of its generalization to the multiplicative dynamics. The aim of the model is to consider the minimal elements for the understanding of the origin of the…
We present an agent based model of a single asset financial market that is capable of replicating several non-trivial statistical properties observed in real financial markets, generically referred to as stylized facts. While previous…
Returning a system to a desired state under a force field involves a thermodynamic cost, i.e., {\it work}. This cost fluctuates for a small-scale system from one experimental realization to another. We introduce a general framework to…
We introduce a stochastic agent-based model for the flocking dynamics of self-propelled particles that exhibit velocity-alignment interactions with neighbours within their field of view. The stochasticity in the dynamics of the model arises…
We present a general framework for modeling a wide selection of flocking scenarios under free boundary conditions. Several variants have been considered - including examples for the widely observed behavior of hierarchically interacting…
We propose that a tree-like hierarchical structure represents a simple and effective way to model the emergent behaviour of financial markets, especially markets where there exists a pronounced intersection between social media influences…
Experiments in predator-prey systems show the emergence of long-term cycles. Deterministic model typically fails in capturing these behaviors, which emerge from the microscopic interplay of individual based dynamics and stochastic effects.…
Urban housing markets, along with markets of other assets, universally exhibit periods of strong price increases followed by sharp corrections. The mechanisms generating such non-linearities are not yet well understood. We develop an…
A new model for stock price fluctuations is proposed, based upon an analogy with the motion of tracers in Gaussian random fields, as used in turbulent dispersion models and in studies of transport in dynamically disordered media. Analytical…
Agent-based models help explain stock price dynamics as emergent phenomena driven by interacting investors. In this modeling tradition, investor behavior has typically been captured by two distinct mechanisms -- learning and heterogeneous…
Understanding the evolutionary stability of cooperation is a central problem in biology, sociology, and economics. There exist only a few known mechanisms that guarantee the existence of cooperation and its robustness to cheating. Here, we…
We propose a novel approach to the statistical analysis of stochastic simulation models and, especially, agent-based models (ABMs). Our main goal is to provide fully automated, model-independent and tool-supported techniques and algorithms…
In this paper, we consider a simple stochastic epidemic model on large regular random graphs and the stochastic process that corresponds to this dynamics in the standard pair approximation. Using the fact that the nodes of a pair are…
We study stochastic particle systems made up of heterogeneous units. We introduce a general framework suitable to analytically study this kind of systems and apply it to two particular models of interest in economy and epidemiology. We show…
The main aim of this work is to incorporate selected findings from behavioural finance into a Heterogeneous Agent Model using the Brock and Hommes (1998) framework. Behavioural patterns are injected into an asset pricing framework through…
In nature and human societies, the effects of homogeneous and heterogeneous characteristics on the evolution of collective behaviors are quite different from each other. It is of great importance to understand the underlying mechanisms of…