p15duering-Accepted.pdf (734.23 kB)
A kinetic equation for economic value estimation with irrationality and herding
journal contribution
posted on 2023-06-09, 01:51 authored by Bertram Duering, Ansgar Jüngel, Lara TrussardiA 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 ModelsISSN
1937-5093Publisher
American Institute of Mathematical SciencesExternal DOI
Issue
1Volume
10Page range
239-261Department 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
2016-06-23First Open Access (FOA) Date
2017-11-02First Compliant Deposit (FCD) Date
2016-06-23Usage metrics
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