相关论文: A fractional reaction-diffusion description of sup…

We present an extended version of the recently proposed "LLOB" model for the dynamics of latent liquidity in financial markets. By allowing for finite cancellation and deposition rates within a continuous reaction-diffusion setup, we…

We revisit the "epsilon-intelligence" model of Toth et al.(2011), that was proposed as a minimal framework to understand the square-root dependence of the impact of meta-orders on volume in financial markets. The basic idea is that most of…

We generalize the reaction-diffusion model A + B -> 0 in order to study the impact of an excess of A (or B) at the reaction front. We provide an exact solution of the model, which shows that linear response breaks down: the average…

We present an agent behavior based microscopic model that induces jumps, spikes and high volatility phases in the price process of a traded asset. We transfer dynamics of thermally activated jumps of an unexcited/ excited two state system…

We propose a dynamical theory of market liquidity that predicts that the average supply/demand profile is V-shaped and {\it vanishes} around the current price. This result is generic, and only relies on mild assumptions about the order flow…

Using Trades and Quotes data from the Paris stock market, we show that the random walk nature of traded prices results from a very delicate interplay between two opposite tendencies: long-range correlated market orders that lead to…

We propose a minimal theory of non-linear price impact based on a linear (latent) order book approximation, inspired by diffusion-reaction models and general arguments. Our framework allows one to compute the average price trajectory in the…

The notion of market impact is subtle and sometimes misinterpreted. Here we argue that impact should not be misconstrued as volatility. In particular, the so-called ``square-root impact law'', which states that impact grows as the…

We present an agent behavior based microscopic model for diffusion price processes. As such we provide a model not only containing a convenient framework for describing socio-economic behavior, but also a sophisticated link to price…

Several models of stock trading [P. Bak et al, Physica A {\bf 246}, 430 (1997)] are analyzed in analogy with one-dimensional, two-species reaction-diffusion-branching processes. Using heuristic and scaling arguments, we show that the…

Based on criteria of mathematical simplicity and consistency with empirical market data, a model with volatility driven by fractional noise has been constructed which provides a fairly accurate mathematical parametrization of the data.…

Understanding anomalous transport and reaction kinetics due to microscopic physical and chemical disorder is a long-standing goal in many fields including geophysics, biology, and engineering. We consider reaction-diffusion characterized by…

In this paper we present an interacting-agent model of stock markets. We describe a stock market through an Ising-like model in order to formulate the tendency of traders getting to be influenced by the other traders' investment attitudes…

It is a well known fact that subdiffusion equations in terms of fractional derivatives can be obtained from Continuous Time Random Walk (CTRW) models with long-tailed waiting time distributions. Over the last years various authors have…

We review the evidence that the erratic dynamics of markets is to a large extent of endogenous origin, i.e. determined by the trading activity itself and not due to the rational processing of exogenous news. In order to understand why and…

In contrast to normal diffusion, there is no canonical model for reactions between chemical species which move by anomalous subdiffusion. Indeed, the type of mesoscopic equation describing reaction-subdiffusion depends on subtle assumptions…

Subdiffusion has been proposed as an explanation of various kinetic phenomena inside living cells. In order to fascilitate large-scale computational studies of subdiffusive chemical processes, we extend a recently suggested mesoscopic model…

We describe a new model to simulate the dynamic interactions between market price and the decisions of two different kind of traders. They possess spatial mobility allowing to group together to form coalitions. Each coalition follows a…

In this paper we present a rather general phenomenological theory of tick-by-tick dynamics in financial markets. Many well-known aspects, such as the L\'evy scaling form, follow as particular cases of the theory. The theory fully takes into…

The financial market is nonpredictable, as according to the Bachelier, the mathematical expectation of the speculator is zero. Nevertheless, we observe in the price fluctuations the two distinct scales, short and long time. Behaviour of a…