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We consider interacting particle systems with unbounded interaction range on general countably infinite graphs $S$ and prove explicit non-asymptotic error bounds for approximations of the infinite-volume dynamics by systems of finitely many…

Probability · Mathematics 2026-03-24 Benedikt Jahnel , Jonas Köppl

The DebtRank algorithm has been increasingly investigated as a method to estimate the impact of shocks in financial networks, as it overcomes the limitations of the traditional default-cascade approaches. Here we formulate a dynamical…

Risk Management · Quantitative Finance 2018-11-21 Marco Bardoscia , Stefano Battiston , Fabio Caccioli , Guido Caldarelli

Density-dependent diffusion is a widespread phenomenon in nature. We have examined the density-dependent diffusion behavior of some biological processes such as tumor growth and invasion [23]. Here, we extend our previous work by developing…

Statistical Mechanics · Physics 2022-02-14 Ahmed M. Fouad , Marwa M. Fouad

We consider diffusion-limited annihilating systems with mobile $A$-particles and stationary $B$-particles placed throughout a graph. Mutual annihilation occurs whenever an $A$-particle meets a $B$-particle. Such systems, when ran in…

Probability · Mathematics 2022-08-05 Riti Bahl , Philip Barnet , Tobias Johnson , Matthew Junge

A system of $N$ weakly interacting particles whose dynamics is given in terms of jump-diffusions with a common factor is considered. The common factor is described through another jump-diffusion and the coefficients of the evolution…

Probability · Mathematics 2015-09-18 A. Budhiraja , E. Kira , Subhamay Saha

We consider a banking network represented by a system of stochastic differential equations coupled by their drift. We assume a core-periphery structure, and that the banks in the core hold a bubbly asset. The banks in the periphery have not…

Mathematical Finance · Quantitative Finance 2018-06-06 Francesca Biagini , Andrea Mazzon , Thilo Meyer-Brandis

This paper is concerned with the problem of budget control in a large particle system modeled by stochastic differential equations involving hitting times, which arises from considerations of systemic risk in a regional financial network.…

Probability · Mathematics 2023-08-30 Erhan Bayraktar , Gaoyue Guo , Wenpin Tang , Yuming Paul Zhang

We consider weakly interacting diffusions on time varying random graphs. The system consists of a large number of nodes in which the state of each node is governed by a diffusion process that is influenced by the neighboring nodes. The…

Probability · Mathematics 2017-02-16 Shankar Bhamidi , Amarjit Budhiraja , Ruoyu Wu

We report a study of a stylized banking cascade model investigating systemic risk caused by counter party failure using liabilities and assets to define banks' balance sheet. In our stylized system, banks can be in two states: normally…

General Finance · Quantitative Finance 2015-06-18 Annika Birch , Tomaso Aste

This paper studies an interacting particle system of interest in econophysics inspired from a model introduced in the physics literature. The original model consists of the customers of a single bank characterized by their capital, and the…

Probability · Mathematics 2022-01-31 Nicolas Lanchier , Stephanie Reed

We study a system of interacting diffusions that models chemotaxis of biological cells or microorganisms (referred to as particles) in a chemical field that is dynamically modified through the collective contributions from the particles.…

Probability · Mathematics 2019-05-01 Amarjit Budhiraja , Wai-Tong Louis Fan

In this paper, we introduce a family of processes with values on the nonnegative integers that describes the dynamics of populations where individuals are allowed to have different types of interactions. The types of interactions that we…

Probability · Mathematics 2020-03-31 Adrián González Casanova , Juan Carlos Pardo , José Luis Perez

We study the limiting behavior of interacting particle systems indexed by large sparse graphs, which evolve either according to a discrete time Markov chain or a diffusion, in which particles interact directly only with their nearest…

Probability · Mathematics 2022-05-18 Daniel Lacker , Kavita Ramanan , Ruoyu Wu

We study a system of self-propelled disks that perform run-and-tumble motion, where particles can adopt more than one internal state. One of those internal states can be transmitted to another particle if the particle carrying this state…

Biological Physics · Physics 2019-12-30 Fernando Peruani , Gustavo Sibona

We consider a system of diffusion processes that interact through their empirical mean and have a stabilizing force acting on each of them, corresponding to a bistable potential. There are three parameters that characterize the system: the…

Risk Management · Quantitative Finance 2012-08-31 Josselin Garnier , George Papanicolaou , Tzu-Wei Yang

This paper constructs a new interacting particle system on a two--dimensional lattice with geometric jumps near a boundary which partially reflects the particles. The projection to each horizontal level is Markov, and on every level the…

Probability · Mathematics 2016-12-20 Jeffrey Kuan

In a previous paper, we applied a field formalism to analyze capital allocation and accumulation within a microeconomic framework of investors and firms. The financial connections were modeled by a field of stakes, representing the links…

Other Condensed Matter · Physics 2025-11-14 Pierre Gosselin , Aïleen Lotz

In this paper we study the distributional properties of a vector of lifetimes in which each lifetime is modeled as the first arrival time between an idiosyncratic shock and a common systemic shock. Despite unlike the classical…

Mathematical Finance · Quantitative Finance 2017-04-17 Sabrina Mulinacci

We consider systems of agents interacting through topological interactions. These have been shown to play an important part in animal andhuman behavior. Precisely, the system consists of a finite number of particles characterized by their…

Mathematical Physics · Physics 2017-11-22 Adrien Blanchet , Pierre Degond

The aim of this paper is to study the large population limit of a binary branching particle system with Moran type interactions: we introduce a new model where particles evolve, reproduce and die independently and, with a probability that…

Probability · Mathematics 2024-04-12 Alexander M. G. Cox , Emma Horton , Denis Villemonais