Related papers: Hydrodynamic limit of order book dynamics
We propose a framework for studying optimal market making policies in a limit order book (LOB). The bid-ask spread of the LOB is modelled by a Markov chain with finite values, multiple of the tick size, and subordinated by the Poisson…
We present a generally covariant formulation of conformal higher-order viscoelastic fluid mechanics with strain allowed to take arbitrarily large values. We give a general prescription to determine the dynamics of a relativistic…
A simple multi-physical system for the potential flow of a fluid through a shroud in which a mechanical component, like a turbine vane, is placed, is modeled mathematically. We then consider a multi criteria shape optimization problem, when…
The paper deals with the asymptotic properties of a random jump process in a high contrast periodic medium in $\mathbb R^d$, $d\geq 1$. We show that if the coordinates of the random jump process in $\mathbb R^d$ are equipped with an extra…
We extend to Markov-modulated Brownian motion (MMBM) the renewal approach which has been successfully applied to the analysis of Markov-modulated fluid models. It has recently been shown that MMBM may be expressed as the limit of a…
We set out a general procedure which allows the approximation of certain Markov chains by the solutions of differential equations. The chains considered have some components which oscillate rapidly and randomly, while others are close to…
This paper is a follow-up of the work initiated in [3], where it has been investigated the hydrodynamic limit of symmetric independent random walkers with birth at the origin and death at the rightmost occupied site. Here we obtain two…
With the proliferation of algorithmic high-frequency trading in financial markets, the Limit Order Book has generated increased research interest. Research is still at an early stage and there is much we do not understand about the dynamics…
We analyze asymptotically a differential-difference equation, that arises in a Markov-modulated fluid model. Here there are N identical sources that turn "on" and "off", and when "on" they generate fluid at unit rate into a buffer, which…
Fluid approximations have seen great success in approximating the macro-scale behaviour of Markov systems with a large number of discrete states. However, these methods rely on the continuous-time Markov chain (CTMC) having a particular…
A continuum model for self-organized dynamics is numerically investigated. The model describes systems of particles subject to alignment interaction and short-range repulsion. It consists of a non-conservative hyperbolic system for the…
We develop a cross-border market model for two countries based on a continuous trading mechanism, in which the transmission capacities that enable transactions between market participants from different countries are limited. Our market…
In this paper we present a novel approach to the determination of fat tails in financial data by studying the information contained in the limit order book. In an order-driven market buyers and sellers may submit limit orders, which are…
We introduce a model for limit order book of a certain security with two main features: First, both the limit orders and market orders for the given asset are allowed to appear and interact with each other. Second, the high frequency…
We study asymmetric zero-range processes on Z with nearest-neighbour jumps and site disorder. The jump rate of particles is an arbitrary but bounded nondecreasing function of the number of particles. For any given environment satisfying…
A well-balanced second-order finite volume scheme is proposed and analyzed for a 2 X 2 system of non-linear partial differential equations which describes the dynamics of growing sandpiles created by a vertical source on a flat, bounded…
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…
We study a system of particles in the interval $[0,\epsilon^{-1}] \cap \mathbb Z$, $\epsilon^{-1}$ a positive integer. The particles move as symmetric independent random walks (with reflections at the endpoints); simultaneously new…
We introduce a structural framework for the geometry of financial order books in which liquidity, supply, and demand are treated as emergent observables rather than primitive market variables. The market is modeled as a relational substrate…
Machine learning methods are being explored in many areas of science, with the aim of finding solution to problems that evade traditional scientific approaches due to their complexity. In general, an order parameter capable of identifying…