A kinetic equation for economic value estimation with irrationality and herding

Düring, Bertram, Jüngel, Ansgar and Trussardi, Lara (2017) A kinetic equation for economic value estimation with irrationality and herding. Kinetic and Related Models, 10 (1). pp. 239-261. ISSN 1937-5093

[img] PDF - Accepted Version
Restricted to SRO admin only until 2 November 2017.

Download (751kB)

Abstract

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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics
Depositing User: Richard Chambers
Date Deposited: 23 Jun 2016 12:09
Last Modified: 13 Mar 2017 12:36
URI: http://sro.sussex.ac.uk/id/eprint/61690

View download statistics for this item

📧 Request an update
Project NameSussex Project NumberFunderFunder Ref
Novel discretisations of higher-order nonlinear PDEG1603LEVERHULME TRUSTRPG-2015-069