On a Kinetic Model for a Simple Market Economy

By Stephane Cordier, Lorenzo Pareschi, Giuseppe Toscani. 2004

267 citations recorded by the source corpus.

In this paper, we consider a simple kinetic model of economy involving both exchanges between agents and speculative trading. We show that the kinetic model admits non trivial quasi-stationary states with power law tails of Pareto type. In order to do this we consider a suitable asymptotic limit of the model yielding a Fokker–Planck equation for the distribution of wealth among individuals. For this equation the stationary state can be easily derived and shows a Pareto power law tail. Numerical results confirm the previous analysis.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/9ccd2b068eab5a4220990b8f59fc128e6f662a25

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Citations in the corpus

Econophysics: Empirical facts and agent-based models (2009, unknown): “…and Yakovenko (2000); Ferrero (2004)), the Boltzmann equation approach (Dragulescu and Yakovenko (2000); Slanina (2004); Repetowicz et al. (2005); Cordier et al. (2005); Matthes and Toscani (2007); Düring and Toscani (2007); Düring et al. (2008)), or Markov chains (Scalas et al. (2006, 2007);…”
Kinetic models of opinion formation (2006, methodology): “Among these Fokker-Planck equations, one is emerging (53) and takes the role of the analogous one obtained in [5, 7] for the evolution of wealth.”
Econophysics review: II. Agent-based models (2011, unknown): “…and Mezard 2000, Dragulescu and Yakovenko 2000, Ferrero 2004), the Boltzmann equation approach (Dragulescu and Yakovenko 2000, Slanina 2004, Cordier et al. 2005, Repetowicz et al. 2005, Düring and Toscani 2007, Matthes and Toscani 2007, Düring et al. 2008), or Markov chains (Scalas et…”
Kinetic models of conservative economies with wealth redistribution (2009, methodology): “Leaving for the moment the problem of approximating the solution of the Boltzmann equation through numerical methods, here we resort to an asymptotic method first introduced in [11] that allows us to recover from the Boltzmann equation a related Fokker-Planck type equation which on one side maintain”
Numerical methods for kinetic equations* (2014, background): “…(Klar and Wegener 1997), tumour immune cell competition (Bellomo and Bellouquid 2004), bacterial movement (Perthame 2007), wealth distributions (Cordier et al. 2005), supply chains (Armbruster, Degond and Ringhofer 2007), flows on networks (Herty and Ringhofer 2011), flocking dynamics (Ha and…”
Colloquium: Statistical mechanics of money, wealth, and income (2009, methodology): “This result was reproduced using a mathematically more involved treatment of this model by Cordier, Pareschi, and Toscani (2005); Pareschi and Toscani (2006).”
Mean Field Games and Applications (2011, background): “One may see [15], [16] or [27] as instances of such an approach.”
Fokker–Planck equations in the modeling of socio-economic phenomena (2017, methodology): “18) has a unique stationary solution of unit mass, given by the Γ-like distribution [18, 36]”
On Steady Distributions of Kinetic Models of Conservative Economies (2008, methodology): “The same effect can be obtained in a more natural way: allow the random variables in (15) to attain arbitrary real values, but discard all trades for which the post-trade money are negative (see the discussion in [13]).”