Delay, feedback and quenching in financial markets
Department of Chemical Engineering, UMIST, PO Box 88, Manchester M60 1QD, UK
Published online: 15 September 2000
An asset whose price exhibits geometric Brownian motion is analysed. The basic Brownian motion model is modified to account for the effects of market delay and investor feedback. A Langevin equation model is appropriate. When the feedback coupling is sufficiently strong, the market dynamics switches from a slow random walk behaviour to a rapid unstable behaviour with a fast time scale characteristic of the market delay. The unstable runaway behaviour is subsequently quenched by investors deserting a collapsing market or saturating a booming one. This quenching effect is sufficient to ensure long term bounding of the asset price. A form of market sabotage is demonstrated in which investors can push the market from a stable to an unstable regime.
PACS: 02.50.Ey – Stochastic processes / 89.90.+n – Other areas of general interest to physicists
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000