Related papers: Conservation Laws in a Limit Order Book
The latent order book of \cite{donier2015fully} is one of the most promising agent-based models for market impact. This work extends the minimal model by allowing agents to exhibit mean-reversion, a commonly observed pattern in real…
A micro-scale model is proposed for the evolution of the limit order book. Within this model, the flows of orders (claims) are described by doubly stochastic Poisson processes taking account of the stochastic character of intensities of bid…
We consider an agent who needs to buy (or sell) a relatively small amount of asset over some fixed short time interval. We work at the highest frequency meaning that we wish to find the optimal tactic to execute our quantity using limit…
We investigate present some new statistical properties of order books. We analyse data from the Nasdaq and investigate (a) the statistics of incoming limit order prices, (b) the shape of the average order book, and (c) the typical life time…
The dynamics of nonlinear conservation laws have long posed fascinating problems. With the introduction of some nonlinearity, e.g. Burgers' equation, discontinuous behavior in the solutions is exhibited, even for smooth initial data. The…
We present a simple, unified approach to determining the growth law for the characteristic length scale, $L(t)$, in the phase ordering kinetics of a system quenched from a disordered phase to within an ordered phase. This approach, based on…
Comparison-based algorithms are algorithms for which the execution of each operation is solely based on the outcome of a series of comparisons between elements. Comparison-based computations can be naturally represented via the following…
The mean-field variant of the model of limit order driven market introduced recently by Maslov is formulated and solved. The agents do not have any strategies and the memory of the system is kept within the order book. We show that he…
In this article we discuss the impact of conservation laws, specifically $U(1)$ charge conservation and energy conservation, on scrambling dynamics, especially on the approach to the late time fully scrambled state. As a model, we consider…
Regardless of a system's complexity or scale, its growth can be considered to be a spontaneous thermodynamic response to a local convergence of down-gradient material flows. Here it is shown how growth can be constrained to a few distinct…
The conservation laws of the third order quasilinear scalar evolution equations are considered via differential system and characteristic cohomology. We find a subspace of 2 forms in the infinite prolonged space in which every conservation…
This paper is devoted to the important yet little explored subject of the market impact of limit orders. Our analysis is based on a proprietary database of metaorders - large orders that are split into smaller pieces before being sent to…
Financial markets can be described on several time scales. We use data from the limit order book of the London Stock Exchange (LSE) to compare how the fluctuation dominated microstructure crosses over to a more systematic global behavior.
In this work we present a rather general approach to approximate the solutions of nonlocal conservation laws. In a first step, we approximate the nonlocal term with an appropriate quadrature rule applied to the spatial discretization. Then,…
Market making (MM) is an important research topic in quantitative finance, the agent needs to continuously optimize ask and bid quotes to provide liquidity and make profits. The limit order book (LOB) contains information on all active…
With the fragmentation of electronic markets, exchanges are now competing in order to attract trading activity on their platform. Consequently, they developed several regulatory tools to control liquidity provision / consumption on their…
We construct Lie point symmetries, a closed-form solution and conservation laws using a non-Noetherian approach for a specific case of the Gorini-Kossakowski-Sudarshan-Lindblad equation that has been recast for the study of non-relativistic…
Individual resource intake rates are known to depend on both individual body size and resource availability. Here, we have developed a model to integrate these two drivers, accounting explicitly for the scaling of perceived resource…
Multi-agent market simulators usually require careful calibration to emulate real markets, which includes the number and the type of agents. Poorly calibrated simulators can lead to misleading conclusions, potentially causing severe loss…
In this paper we explore the theoretical boundaries of planning in a setting where no model of the agent's actions is given. Instead of an action model, a set of successfully executed plans are given and the task is to generate a plan that…