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We use standard physics techniques to model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties of a market, such as the diffusion rate of prices, which is the standard measure of financial risk, and the spread and price impact functions, which are the main determinants of transaction cost. Guided by dimensional analysis, simulation, and mean field theory, we find scaling relations in terms of order flow rates. We show that even under completely random order flow the need to store supply and demand to facilitate trading induces anomalous diffusion and temporal structure in prices.
The dynamics of a stock market with heterogeneous agents is discussed in the framework of a recently proposed spin model for the emergence of bubbles and crashes. We relate the log returns of stock prices to magnetization in the model and find that i
We investigate the herd behavior of returns for the yen-dollar exchange rate in the Japanese financial market. It is obtained that the probability distribution $P(R)$ of returns $R$ satisfies the power-law behavior $P(R) simeq R^{-beta}$ with the exp
Trading frictions are stochastic. They are, moreover, in many instances fast-mean reverting. Here, we study how to optimally trade in a market with stochastic price impact and study approximations to the resulting optimal control problem using singul
We study an economic model where agents trade a variety of products by using one of three competing rules: need, greed and noise. We find that the optimal strategy for any agent depends on both product composition in the overall market and compositio
A self-organized model with social percolation process is proposed to describe the propagations of information for different trading ways across a social system and the automatic formation of various groups within market traders. Based on the market