Related papers: Particle systems with singular interaction through…
We introduce a family of particle systems on sparse graphs where local interactions occur via hitting times, providing a dynamic and tractable model for default cascades in large sparsely-connected financial networks. Building on the…
Building on the line of work [DIRT15a], [DIRT15b], [NS17a], [DT17], [HLS18], [HS18] we continue the study of particle systems with singular interaction through hitting times. In contrast to the previous research, we (i) consider very…
We study an interacting particle system whose dynamics depends on an interacting random environment. As the number of particles grows large, the transition rate of the particles slows down (perhaps because they share a common resource of…
We study the existence and the exponential ergodicity of a general interacting particle system, whose components are driven by independent diffusion processes with values in an open subset of $\mathds{R}^d$, $d\geq 1$. The interaction…
We consider a dynamic model of interconnected banks. New banks can emerge, and existing banks can default, creating a birth-and-death setup. Microscopically, banks evolve as independent geometric Brownian motions. Systemic effects are…
A simple banking network model is proposed which features multiple waves of bank defaults and is analytically solvable in the limiting case of an infinitely large homogeneous network. The model is a collection of nodes representing…
Systemic risk in banking systems remains a crucial issue that it has not been completely understood. In our toy model, banks are exposed to two sources of risks, namely, market risk from their investments in assets external to the banking…
In this paper we consider three classes of interacting particle systems on $\mathbb Z$: independent random walks, the exclusion process, and the inclusion process. We allow particles to switch their jump rate (the rate identifies the type…
We consider the problem of governing systemic risk in a banking system model. The banking system model consists in an initial value problem for a system of stochastic differential equations whose dependent variables are the log-monetary…
We give a general existence and convergence result for interacting particle systems on locally finite graphs with possibly unbounded degrees or jump rates. We allow the local state space to be Polish, and the jumps at a site to affect the…
We introduce an interacting particle system that models the spread of an epidemic in terms of heterogeneous diffusive dynamics, rather than exogenous contact and transmission rates at the population level as in classical compartmental…
We consider the problem of governing systemic risk in an assets-liabilities dynamical model of banking system. In the model considered each bank is represented by its assets and its liabilities.The capital reserves of a bank are the…
We study finite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which…
In this paper we consider an interacting particle system modeled as a system of $N$ stochastic differential equations driven by Brownian motions with a drift term including a confining potential acting on each particle, and an interaction…
We consider a general framework for multi-type interacting particle systems on graphs, where particles move one at a time by random walk steps, different types may have different speeds, and may interact, possibly randomly, when they meet.…
Complex non-linear interactions between banks and assets we model by two time-dependent Erd\H{o}s Renyi network models where each node, representing bank, can invest either to a single asset (model I) or multiple assets (model II). We use…
An interbank market lets participants pool the risk arising from the combination of illiquid investments and random withdrawals by depositors. But it also creates the potential for one bank's failure to trigger off avalanches of further…
We consider a rate control problem for an $N$-particle weakly interacting finite state Markov process. The process models the state evolution of a large collection of particles and allows for multiple particles to change state…
In this paper we consider a mean-field model of interacting diffusions for the monetary reserves in which the reserves are subjected to a self- and cross-exciting shock. This is motivated by the financial acceleration and fire sales…
Consider an interacting particle system indexed by the vertices of a (possibly random) locally finite graph whose vertices and edges are equipped with marks representing parameters of the model such as the environment and initial…