Abstract

An asset whose prier exhibits geometric Brownian motion is analysed. The basic Brownian motion model is modified tu 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.