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A kinetic equation for economic value estimation with irrationality and herding

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posted on 2023-06-09, 01:51 authored by Bertram Duering, Ansgar Jüngel, Lara Trussardi
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.

Funding

Novel discretisations of higher-order nonlinear PDE; G1603; LEVERHULME TRUST; RPG-2015-069

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Kinetic and Related Models

ISSN

1937-5093

Publisher

American Institute of Mathematical Sciences

Issue

1

Volume

10

Page range

239-261

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Numerical Analysis and Scientific Computing Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2016-06-23

First Open Access (FOA) Date

2017-11-02

First Compliant Deposit (FCD) Date

2016-06-23

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