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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Received 24 February 2000
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Grassia, P. Delay, feedback and quenching in financial markets. Eur. Phys. J. B 17, 347–362 (2000). https://doi.org/10.1007/s100510070151
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DOI: https://doi.org/10.1007/s100510070151