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Investigations to the dynamics of wealth distribution in a kinetic exchange model

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  • Zhong, Yue
  • Lai, Shaoyong
  • Hu, Chunhua

Abstract

A kinetic exchange model is used to investigate the evolution of wealth distribution in a financial market. Assume that the market is characterized by a risky asset (a stock) and a risk-less asset (a bond). The model captures wealth exchanges and speculative trading to affect the dynamics of wealth distribution. We embed a suitable value function into the interactions of wealth to describe that agents allocate their wealth between the risky and risk-less assets. The value function contains the predicted price and present price of the stock to depict reactions of agents toward potential risks. The price prediction and risk estimation affect investment strategies of agents through the value function. After constructing the interactions of wealth, we apply quasi-invariant wealth limits and Boltzmann-type equations to derive a Fokker-Planck equation with underlying equilibrium. When the wealth invested in the risky asset satisfies certain conditions, an explicit stationary solution of the Fokker-Planck equation is obtained to show that the wealth distribution converges exponentially to a close lognormal distribution in the long run. Numerical experiments are given to illustrate our results.

Suggested Citation

  • Zhong, Yue & Lai, Shaoyong & Hu, Chunhua, 2021. "Investigations to the dynamics of wealth distribution in a kinetic exchange model," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    • Handle: RePEc:eee:apmaco:v:404:y:2021:i:c:s0096300321003210
    DOI: 10.1016/j.amc.2021.126231
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