A kinetic equation for economic value estimation with irrationality and herding

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2017
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Düring, Bertram
Jüngel, Ansgar
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Kinetic & Related Models. American Institute of Mathematical Sciences (AIMS). 2017, 10(1), pp. 239-261. ISSN 1937-5093. eISSN 1937-5077. Available under: doi: 10.3934/krm.2017010
Zusammenfassung

A kinetic inhomogeneous Boltzmann-type equation is proposed to model the dynamics of the number of agents in a large market depending on the estimated value of an asset and the rationality of the agents. The interaction rules take into account the interplay of the agents with sources of public information, herding phenomena, and irrationality of the individuals. In the formal grazing collision limit, a nonlinear nonlocal Fokker-Planck equation with anisotropic (or incomplete) diffusion is derived. The existence of global-in-time weak solutions to the Fokker-Planck initial-boundary-value problem is proved. Numerical experiments for the Boltzmann equation highlight the importance of the reliability of public information in the formation of bubbles and crashes. The use of Bollinger bands in the simulations shows how herding may lead to strong trends with low volatility of the asset prices, but eventually also to abrupt corrections.

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Fachgebiet (DDC)
510 Mathematik
Schlagwörter
Inhomogeneous Boltzmann equation, public information, herding, Fokker-Planck equation, existence of solutions, sociophysics.
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ISO 690DÜRING, Bertram, Ansgar JÜNGEL, Lara TRUSSARDI, 2017. A kinetic equation for economic value estimation with irrationality and herding. In: Kinetic & Related Models. American Institute of Mathematical Sciences (AIMS). 2017, 10(1), pp. 239-261. ISSN 1937-5093. eISSN 1937-5077. Available under: doi: 10.3934/krm.2017010
BibTex
@article{During2017kinet-55537,
  year={2017},
  doi={10.3934/krm.2017010},
  title={A kinetic equation for economic value estimation with irrationality and herding},
  number={1},
  volume={10},
  issn={1937-5093},
  journal={Kinetic & Related Models},
  pages={239--261},
  author={Düring, Bertram and Jüngel, Ansgar and Trussardi, Lara}
}
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