Related papers: A prognosis oriented microscopic stock market mode…
We propose a model for equity trading in a population of agents where each agent acts to achieve his or her target stock-to-bond ratio, and, as a feedback mechanism, follows a market adaptive strategy. In this model only a fraction of…
We analyze a tractable model of a limit order book on short time scales, where the dynamics are driven by stochastic fluctuations between supply and demand. We establish the existence of a limiting distribution for the highest bid, and for…
A prototype model of stock market is introduced and studied numerically. In this self-organized system, we consider only the interaction among traders without external influences. Agents trade according to their own strategy, to accumulate…
This paper presents a framework of imitating the principal investor's behavior for optimal pricing and hedging options. We construct a non-deterministic Markov decision process for modeling stock price change driven by the principal…
Price fluctuations in financial markets can be characterized by L\'evy's stable distribution, which is supported by the generalized central limit system. When the stable parameters were estimated from four different stock markets in long…
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…
We develop a behavioral model for liquidity and volatility based on empirical regularities in trading order flow in the London Stock Exchange. This can be viewed as a very simple agent based model in which all components of the model are…
We present a mathematical model of a market with $m$ shares traded across $n$ investor groups, each one with similar motivations and trading strategies. The market of each asset consists of a fixed amount of cash and shares (no additions…
We consider the problem of supply and demand balancing that is stated as a minimization problem for the total expected revenue function describing the behavior of both consumers and suppliers. In the considered market model we assume that…
Using available data from the New York stock market (NYSM) we test four different bi-parametric models to fit the correspondent volume-price distributions at each $10$-minute lag: the Gamma distribution, the inverse Gamma distribution, the…
We introduce solvable stochastic dealer models, which can reproduce basic empirical laws of financial markets such as the power law of price change. Starting from the simplest model that is almost equivalent to a Poisson random noise…
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 study an agent-based stock market model with heterogeneous agents and friction. Our model is based on that of Foellmer-Schweizer(1993): The process of a stock price in a discrete-time framework is determined by temporary equilibria via…
In this paper we demonstrate a striking regularity in the way people place limit orders in financial markets, using a data set consisting of roughly seven million orders from the London Stock Exchange. We define the relative limit price as…
A statistical generalization is made of microeconomics in the spirit of going from classical to statistical mechanics. The price and quantity of every commodity1 traded in the market, at each instant of time, is considered to be an…
This article considers a model for alternative processes for securities prices and compares this model with actual return data of several securities. The distributions of returns that appear in the model can be Gaussian as well as…
This paper studies a continuous-time market {under stochastic environment} where an agent, having specified an investment horizon and a target terminal mean return, seeks to minimize the variance of the return with multiple stocks and a…
We develop from basic economic principles a continuous-time model for a large investor who trades with a finite number of market makers at their utility indifference prices. In this model, the market makers compete with their quotes for the…
We present an empirical study of the subordination hypothesis for a stochastic time series of a stock price. The fluctuating rate of trading is identified with the stochastic variance of the stock price, as in the continuous-time random…
A new model for stocks markets using integer values for each stock price is presented. In contrast with previously reported models, the variables used in the model are not of binary type, but of more general integer type. It is shown how…