Related papers: Long time behaviour and mean-field limit of Atlas …

The mean-field limit of systems of rank-based interacting diffusions is known to be described by a nonlinear diffusion process. We obtain a similar description at the level of stationary distributions. Our proof is based on explicit…

We study a mean-field version of rank-based models of equity markets such as the Atlas model introduced by Fernholz in the framework of Stochastic Portfolio Theory. We obtain an asymptotic description of the market when the number of…

We propose a set of conservative models in which agents exchange wealth with a preference in the choice of interacting agents in different ways. The common feature in all the models is that the temporary values of financial status of agents…

This paper analyzes and explicitly solves a class of long-term average impulse control problems with a specific mean-field interaction. The underlying process is a general one-dimensional diffusion with appropriate boundary behavior. The…

Agent-based models are a natural choice for modeling complex social systems. In such models simple stochastic interaction rules for a large population of individuals can lead to emergent dynamics on the macroscopic scale, for instance a…

Atlas-type models are constant-parameter models of uncorrelated stocks for equity markets with a stable capital distribution, in which the growth rates and variances depend on rank. The simplest such model assigns the same, constant…

In this work the system of agents is applied to establish a model of the nonlinear distributed signal processing. The evolution of the system of the agents - by the prediction time scale diversified trend followers, has been studied for the…

Factor models characterize the joint behavior of large sets of financial assets through a smaller number of underlying drivers. We develop a network-based framework in which factors emerge naturally from the structure of interactions among…

We study the limiting behaviour of the empirical measure of a system of diffusions interacting through their ranks when the number of diffusions tends to infinity. We prove that the limiting dynamics is given by a McKean-Vlasov evolution…

A broad set of empirical phenomenon in the study of social, economic and machine behaviour can be modelled as complex systems with averaging dynamics. However many of these models naturally result in consensus or consensus-like outcomes. In…

We study Atlas-type models of equity markets with local characteristics that depend on both name and rank, and in ways that induce a stable capital distribution. Ergodic properties and rankings of processes are examined with reference to…

We study in detail a one-dimensional lattice model of a continuum, conserved field (mass) that is transferred deterministically between neighbouring random sites. The model falls in a wider class of lattice models capturing the joint effect…

We introduce a mean-field framework for the study of systems of interacting particles sharing a conserved quantity. The work generalises and unites the existing fields of asset-exchange models, often applied to socio-economic systems, and…

The question how social norms can emerge from microscopic interactions between individuals is a key problem in social sciences to explain collective behavior. In this paper we propose an agent-based model to show that randomly distributed…

Agent-based modeling is a powerful simulation technique to understand the collective behavior and microscopic interaction in complex financial systems. Recently, the concept for determining the key parameters of the agent-based models from…

Atlas models are systems of Ito processes with parameters that depend on rank. We show that the parameters of a simple Atlas model can be identified by measuring the variance of the top-ranked process for different sampling intervals.

We introduce and study a nonlinear discrete dynamical system describing the evolution of a resource distribution among interacting agents. The model generalizes several classical mean-field and opinion-dynamics frameworks and is defined on…

We define data-driven macroeconomic regimes by clustering the relative performance in time of indices belonging to different asset classes. We then investigate lead-lag relationships within the regimes identified. Our study unravels market…

An agent-based model is proposed for analyzing the dynamics that arise from interactions within social networks, analyzing the individual behavior of each profile. Said model considers a simplified construction of a social network while…

We develop an agent-based model on a lattice to investigate territorial development motivated by markings such as graffiti, generalizing a previously-published model to account for $K$ groups instead of two groups. We then analyze this…