Abstract
We introduce and discuss a new kinetic system for a financial market composed by agents that may belong to two different trader populations, whose behavior determines the price dynamic of a certain stock. Our mesoscopic description is based on the microscopic Lux--Marchesi model [16,17], and share analogies with the recent kinetic model by Maldarella and Pareschi [18], from which it differs in various points. In particular, it takes into account price acceleration, as well as a microscopic binary interaction for the exchange between the two populations of agents. Various numerical simulations show that the model can describe realistic situations, like regimes of boom and crashes, as well as the invariance of the large-time behavior with respect to the number of agents of the market.
Highlights
Agent-based models represent a broad class of mathematical models which have been recently considered to describe various phenomena of economic dynamics
Starting from the microscopic dynamics, kinetic models for trading can be derived with the tools of classical kinetic theory of fluids [7, 10, 11, 20, 24], where kinetic econophysics has been treated in the framework of Boltzmann-like equation for Maxwell-type molecules
Still resorting to the classical methods of kinetic theory, we introduce a model which is reminiscent of both Lux–Marchesi [16, 17] and Maldarella–Pareschi [18] ideas
Summary
Agent-based models represent a broad class of mathematical models which have been recently considered to describe various phenomena of economic dynamics. By taking the mean with respect to the opinion variable, we obtain the average investment propensity X(t) of chartists, defined by
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