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In this paper, we study the evolution of iterated equilibrium distributions for the Gamma and Weibull families of distributions as the iteration step increases. We characterize their moments and the pointwise limit of the distribution…
We propose some kinetic models of wealth exchange and investigate their behavior on directed networks though numerical simulations. We observe that network topology and directedness yields a variety of interesting features in these models.…
This paper analyzes the equilibrium distribution of wealth in an economy where firms' productivities are subject to idiosyncratic shocks, returns on factors are determined in competitive markets, dynasties have linear consumption functions…
We construct explicit invariant measures for a family of infinite products of random, independent, identically-distributed elements of SL(2,C). The matrices in the product are such that one entry is gamma-distributed along a ray in the…
The agent-based Yard-Sale model of wealth inequality is generalized to incorporate exponential economic growth and its distribution. The distribution of economic growth is nonuniform and is determined by the wealth of each agent and a…
A dynamical model of capital exchange is introduced in which a specified amount of capital is exchanged between two individuals when they meet. The resulting time dependent wealth distributions are determined for a variety of exchange…
We study a generalization of the model of a dark market due to Duffie-G\^arleanu- Pedersen [6]. Our market is segmented and involves multiple assets. We show that this market has a unique asymptotically stable equilibrium. In order to…
Motivated by the need for parametric families of rich and yet tractable distributions in financial mathematics, both in pricing and risk management settings, but also considering wider statistical applications, we investigate a novel…
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…
Adam Smith's inquiry into the emergence and stability of the self-organization of the division of labor in commodity production and exchange is considered using statistical equilibrium methods from statistical physics. We develop a…
We study in detail and explicitly solve the version of Kyle's model introduced in a specific case in \cite{BB}, where the trading horizon is given by an exponentially distributed random time. The first part of the paper is devoted to the…
A new discrete distribution has been proposed as a discrete analogue of the two sided power distribution [Van Drop, J. R. and Kotz, S. (2002a). A novel extension of the triangular distribution and its parameter estimation, Journal of the…
We analyze a class of energy and wealth redistribution models. We characterize their stationary measures and show that they have a discrete dual process. In particular we show that the wealth distribution model with non-zero propensity can…
We study the model of interacting agents proposed by Chatterjee et al that allows agents to both save and exchange wealth. Closed equations for the wealth distribution are developed using a mean field approximation. We show that when all…
We model a closed economic system with interactions that generates the features of empirical wealth distribution across all wealth brackets, namely a Gibbsian trend in the lower and middle wealth range and a Pareto trend in the higher…
An infinite convergent sum of independent and identically distributed random variables discounted by a multiplicative random walk is called perpetuity, because of a possible actuarial application. We give three disjoint groups of sufficient…
This article describes mathematical methods for estimating the top-tail of the wealth distribution and therefrom the share of total wealth that the richest $p$ percent hold, which is an intuitive measure of inequality. As the data base for…
We present a detailed numerical analysis of the modified version of a conservative self-organized extremal model introduced by Pianegonda et. al. for the distribution of wealth of the people in a society. Here the trading process has been…
We investigate the accumulated wealth distribution by adopting evolutionary games taking place on scale-free networks. The system self-organizes to a critical Pareto distribution (1897) of wealth $P(m)\sim m^{-(v+1)}$ with $1.6 < v <2.0$…
We propose a simple dynamical model of wealth evolution. The invariant distributions are of Pareto type and are dynamically stable as conjectured by Pareto.