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We give a microscopic representation of the stock-market in which the microscopic agents are the individual traders and their capital. Their basic dynamics consists in the auto-catalysis of the individual capital and in the global…
Power-law distributions with various exponents are studied. We first introduce a simple and generic model that reproduces Zipf's law. We can regard this model both as the time evolution of the population of cities and that of the asset…
We use data on wealth of the richest persons taken from the "rich lists" provided by business magazines like Forbes to verify if upper tails of wealth distributions follow, as often claimed, a power-law behaviour. The data sets used cover…
We have numerically simulated the ideal-gas models of trading markets, where each agent is identified with a gas molecule and each trading as an elastic or money-conserving two-body collision. Unlike in the ideal gas, we introduce…
We discuss the ideal gas like models of a trading market. The effect of savings on the distribution have been thoroughly reviewed. The market with fixed saving factors leads to a Gamma-like distribution. In a market with quenched random…
This paper studies stochastic mechanisms under which light-tailed latent price dynamics yield realized prices with power-law tails. The realized price is modeled as $P_T=e^{X_T}$, where $X$ is a Markov-modulated L\'evy process and $T$ is…
In the manuscript, we are interested in using kinetic theory to better understand the time evolution of wealth distribution and their large scale behavior such as the evolution of inequality (e.g. Gini index). We investigate three type of…
In this study, we investigate the statistical properties of the returns and the trading volume. We show a typical example of power-law distributions of the return and of the trading volume. Next, we propose an interacting agent model of…
In our model, $n$ traders interact with each other and with a central bank; they are taxed on the money they make, some of which is dissipated away by corruption. A generic feature of our model is that the richest trader always wins by…
We present a simplified model for the exploitation of finite resources by interacting agents, where each agent receives a random fraction of the available resources. An extremal dynamics ensures that the poorest agent has a chance to change…
We study the optimal decisions and equilibria of agents who aim to minimize their risks by allocating their positions over extremely heavy-tailed (i.e., infinite-mean) and possibly dependent losses. The loss distributions of our focus are…
In capitalist societies, only a single right can be fully exerted without constraints of any kind: the limitless accumulation of wealth. Such imperative or prime axiom is the ultimate cause of the raising waves of inequalities observed…
We construct a model of wealth distribution, based on an interactive multiplicative stochastic process on static complex networks. Through numerical simulations we show that a decrease in the number of links discourages equality in wealth…
The recent book by T. Piketty (Capital in the Twenty-First Century) promoted the important issue of wealth inequality. In the last twenty years, physicists and mathematicians developed models to derive the wealth distribution using discrete…
We study here numerically the behavior of an ideal gas like model of markets having only one non-consumable commodity. We investigate the behavior of the steady-state distributions of money, commodity and total wealth, as the dynamics of…
This paper consider a highly general dissemination model that keeps track of the stochastic evolution of the distribution of wealth over a set of agents. There are two types of events: (i) units of wealth externally arrive, and (ii) units…
We investigate the transient and steady-state dynamics of the Bennati-Dragulescu-Yakovenko money game in the presence of probabilistic cheaters, who can misrepresent their financial status by claiming to have no money. We derive the…
We discuss the equivalence between kinetic wealth-exchange models, in which agents exchange wealth during trades, and mechanical models of particles, exchanging energy during collisions. The universality of the underlying dynamics is shown…
Scaling properties in financial fluctuations are reviewed from the standpoint of statistical physics. We firstly show theoretically that the balance of demand and supply enhances fluctuations due to the underlying phase transition…
We study a model of wealth dynamics [Bouchaud and M\'ezard 2000, \emph{Physica A} \textbf{282}, 536] which mimics transactions among economic agents. The outcomes of the model are shown to depend strongly on the topological properties of…