Related papers: Jump diffusion approximation for the price dynamic…
We consider the stochastic ranking process with space-time dependent jump rates for the particles. The process is a simplified model of the time evolution of the rankings such as sales ranks at online bookstores. We prove that the joint…
In the present paper the macroscopic limits of the kinetic model for inter-acting entities (individuals, organisms, cells) are studied. The kinetic model is one-dimensional and entities are characterized by their position and orientation…
Despite the fact that an intraday market price distribution is not normal, the random walk model of price behaviour is as important for the understanding of basic principles of the market as the pendulum model is a starting point of many…
This paper establishes limit theorems for a class of stochastic hybrid systems (continuous deterministic dynamic coupled with jump Markov processes) in the fluid limit (small jumps at high frequency), thus extending known results for jump…
We study diffusive mixing in the presence of thermal fluctuations under the assumption of large Schmidt number. In this regime we obtain a limiting equation that contains a diffusive thermal drift term with diffusion coefficient obeying a…
This article provides a simple explanation of the asymptotic concavity of the price impact of a meta-order via the microstructural properties of the market. This explanation is made more precise by a model in which the local relationship…
Order book dynamics play an important role in both execution time and price formation of orders in an exchange market. In this study, we aim to model the limit order arrival rates in the vicinity of the best bid and the best ask price…
We study a totally asymmetric simple exclusion process where jumps happen at rate one, except at the origin where the rate is lower. We prove a hydrodynamic scaling limit to a macroscopic profile described by a variational formula. The…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
This paper investigates real-time detection of spoofing activity in limit order books, focusing on cryptocurrency centralized exchanges. We first introduce novel order flow variables based on multi-scale Hawkes processes that account both…
Research on limit order book markets has been rapidly growing and nowadays high-frequency full order book data is widely available for researchers and practitioners. However, it is common that research papers use the best level data only,…
We present results of numerical analysis of several simple models for the microstructure of a double auction market without intermediaries which were introduced in cond-mat/9808240. We perform computer simulations of the minimal model in…
We analyze a pair of diffusion equations which are derived in the infinite system--size limit from a microscopic, individual--based, stochastic model. Deviations from the conventional Fickian picture are found which ultimately relate to the…
We consider the problem of dynamic pricing with limited supply. A seller has $k$ identical items for sale and is facing $n$ potential buyers ("agents") that are arriving sequentially. Each agent is interested in buying one item. Each…
Managing high-frequency data in a limit order book (LOB) is a complex task that often exceeds the capabilities of conventional time-series forecasting models. Accurately predicting the entire multi-level LOB, beyond just the mid-price, is…
The present works is focused on studying bifurcating solutions in compressible fluid dynamics. On one side, the physics of the problem is thoroughly investigated using high-fidelity simulations of the compressible Navier-Stokes equations…
Constraints can affect dramatically the behavior of diffusion processes. Recently, we analyzed a natural and a technological system and reported that they perform diffusion-like discrete steps displaying a peculiar constraint, whereby the…
The scaling invariance for chaotic orbits near a transition from unlimited to limited diffusion in a dissipative standard mapping is explained via the analytical solution of the diffusion equation. It gives the probability of observing a…
Many commonly used liquidity measures are based on snapshots of the state of the limit order book (LOB) and can thus only provide information about instantaneous liquidity, and not regarding the local liquidity regime. However, trading in…
In this article we revisit the classic problem of tatonnement in price formation from a microstructure point of view, reviewing a recent body of theoretical and empirical work explaining how fluctuations in supply and demand are slowly…