Delay, feedback and quenching in financial markets

Grassia, P.S. (2000) Delay, feedback and quenching in financial markets. European Physical Journal B - Condensed Matter and Complex Systems, 17 (2). pp. 347-362. ISSN 1434-6028 (https://doi.org/10.1007/s100510070151)

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Abstract

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.

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