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Financial market is an example of complex system, which is characterized by a highly intricate organization and the emergence of collective behavior. In this paper, we quantify this emergent dynamics in the financial market by using…
We propose a numerical method for approximate calculations of the time evolution of point particle systems given only the system's Hamiltonian function and initial conditions. The method both generates and solves the equations of motion…
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…
Financial markets are an intriguing place that offer investors the potential to gain large profits if timed correctly. Unfortunately, the dynamic, non-linear nature of financial markets makes it extremely hard to predict future price…
We model the price of a stock via a Lang\'{e}vin equation with multi-dimensional fluctuations coupled in the price and in time. We generalize previous models in that we assume that the fluctuations conditioned on the time step are compound…
This paper considers a simulation-based estimator for a general class of Markovian processes and explores some strong consistency properties of the estimator. The estimation problem is defined over a continuum of invariant distributions…
We present an outlook of the studies on correlations in the price timeseries of stocks, discussing the construction and applications of "asset tree". The topic discussed here should illustrate how the complex economic system (financial…
We present several models to describe the stochastic evolution of stocks that show some strong resistance at some level and generalize to this situation the evolution based upon geometric Brownian motion. If volatility and drift are related…
We generalize Taylor's theorem by introducing a stochastic formulation based on an underlying Poisson point process model. We utilize this approach to propose a novel non-linear regression framework and perform statistical inference of the…
We introduce and study a simple model of a limit order-driven market. Traders in this model can either trade at the market price or place a limit order, i.e. an instruction to buy (sell) a certain amount of the stock if its price falls…
The paper discusses a path-wise approach to stock price modelling.
An agent-based modelling methodology for the joint price evolution of two stocks is put forward. The method models future multidimensional price trajectories reflecting how a class of agents rebalance their portfolios in an operational way…
In this paper, we study the portfolio optimization problem with general utility functions and when the return and volatility of underlying asset are slowly varying. An asymptotic optimal strategy is provided within a specific class of…
The geometric approach to financial markets with proportional transaction cost prescribes to imbed a specific model (of stock market, of currency market etc.), usually given in a parametric form, into a natural framework defined by the two…
We present a dynamical model for the price evolution of financial assets. The model is based in a two level structure. In the first stage one finds an agent-based model that describes the present state of the investors' beliefs,…
Constant and symmetric price impact functions, most commonly used in agent-based market modelling, are shown to give rise to paradoxical and inconsistent outcomes in the simplest case of arbitrage exploitation when open-hold-close actions…
We reformulate the Cont-Bouchaud model of financial markets in terms of classical "super-spins" where the spin value is a measure of the number of individual traders represented by a portfolio manager of an investment agency. We then extend…
We present a new microscopic stochastic model for an ensemble of interacting investors that buy and sell stocks in discrete time steps via limit orders based on individual forecasts about the price of the stock. These orders determine the…
A new multiagent model of the stock market is formulated that contains four states in which the agents may be located. Next, the model is reformulated in the language of the functional integral containing fluctuations of prices and…
This paper reports the effort of using agent-based mix-game model to predict financial time series. It introduces simple generic algorithm into the prediction methodology, and gives an example of its application to forecasting Shanghai…