Masanao Aoki developed a new methodology for a basic problem of economics: deducing rigorously the macroeconomic dynamics as emerging from the interactions of many individual agents. This includes deduction of the fractal / intermittent fluctuations of macroeconomic quantities from the...

We study analytically and numerically Minsky instability as a combination of top-down, bottom-up and peer-to-peer positive feedback loops. The peer-to-peer interactions are represented by the links of a network formed by the connections between firms, contagion leading to avalanches and...

Most real life systems have a random component: the multitude of endogenous and exogenous factors influencing them result in stochastic fluctuations of the parameters determining their dynamics. These empirical systems are in many cases subject to noise of multiplicative nature. The special...

We show that a simple and intuitive three-parameter equation fits remarkably well the evolution of the gross domestic product (GDP) in current and constant dollars of many countries during times of recession and recovery. We then argue that this equation is the response function of the economy...

Financial time series typically exhibit strong fluctuations that cannot be described by a Gaussian distribution. In recent empirical studies of stock market indices it was examined whether the distribution P(r) of returns r(tau) after some time tau can be described by a (truncated) Levy-stable...

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 competition/cooperation between the agents mediated by the total...

We study the finite-size effects in some scaling systems, and show that the finite number of agents N leads to a cut-off in the upper value of the Pareto law for the relative individual wealth. The exponent $\alpha$ of the Pareto law obtained in stochastic multiplicative market models is...

The dynamics of generalized Lotka-Volterra systems is studied by theoretical techniques and computer simulations. These systems describe the time evolution of the wealth distribution of individuals in a society, as well as of the market values of firms in the stock market. The individual wealths...

Proving the existence of speculative financial bubbles even a posteriori has proven exceedingly difficult so anticipating a speculative bubble ex ante would at first seem an impossible task. Still as illustrated by the recent turmoil in financial markets initiated by the so called subprime...

Using a model based on generalised Lotka Volterra dynamics together with some recent results for the solution of generalised Langevin equations, we show that the equilibrium solution for the probability distribution of wealth has two characteristic regimes. For large values of wealth it takes...