Related papers: Evolution and anti-evolution in a minimal stock ma…
We reverse-engineer the equilibrium construction process of asset prices in order to obtain returns which depend on firm characteristics, possibly in a linear fashion. One key requirement is that agents must have demands that rely…
Keeping a basic tenet of economic theory, rational expectations, we model the nonlinear positive feedback between agents in the stock market as an interplay between nonlinearity and multiplicative noise. The derived hyperbolic stochastic…
In this review article we explore several recent advances in the quantitative modeling of financial markets. We begin with the Efficient Markets Hypothesis and describe how this controversial idea has stimulated a number of new directions…
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
The aim of this paper is to propose a heterogeneous agent model of stock markets that develop complicated endogenous price fluctuations. We find occurrences of non-stationary chaos, or speculative bubble, are caused by the heterogeneity of…
Different agents need to make a prediction. They observe identical data, but have different models: they predict using different explanatory variables. We study which agent believes they have the best predictive ability -- as measured by…
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…
How can a microorganism adapt to a variety of environmental conditions despite there exists a limited number of signal transduction machineries? We show that for any growing cells whose gene expression is under stochastic fluctuations,…
We present long Monte Carlo simulations of a simple model of biological macroevolution in which births, deaths, and mutational changes in the genome take place at the level of individual organisms. The model displays punctuated equilibria…
The concept of fitness as a measure for a species's success in natural selection is central to the theory of evolution. We here investigate how reproduction rates which are not constant but vary in response to environmental fluctuations,…
We model an informed agent with information about the future value of an asset trying to maximize profits when subjected to a transaction cost as well as a market maker tasked with setting fair transaction prices. In a single auction model,…
Financial time series often exhibit low signal-to-noise ratio, posing significant challenges for accurate data interpretation and prediction and ultimately decision making. Generative models have gained attention as powerful tools for…
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…
This paper presents an agent based model of an electronic market with two types of trading agents. One type follows a mean reverting strategy and the other, the speculative trader, tracks the maximum realised return over recent trades. The…
A novel approach to analyzing time series generated by complex systems, such as markets, is presented. The basic idea of the approach is the {\it Law of Self-Similar Evolution}, according to which any complex system develops self-similarly.…
This paper develops a comprehensive theoretical framework that imports concepts from stochastic thermodynamics to model price impact and characterize the feasibility of round-trip arbitrage in financial markets. A trading cycle is treated…
We explore a decomposition in which returns on a large class of portfolios relative to the market depend on a smooth non-negative drift and changes in the asset price distribution. This decomposition is obtained using general continuous…
Quantitative finance has had a long tradition of a bottom-up approach to complex systems inference via multi-agent systems (MAS). These statistical tools are based on modelling agents trading via a centralised order book, in order to…
We discuss how minimal financial market models can be constructed by bridging the gap between two existing, but incomplete, market models: a model in which a population of virtual traders make decisions based on common global information…
We show that a simple model of a spatially resolved evolving economic system, which has a steady state under simultaneous updating, shows stable oscillations in price when updated asynchronously. The oscillations arise from a gradual…