Reaction-diffusion-branching models of stock price fluctuations

Lei Han Tang; Guang Shan Tian

doi:10.1016/S0378-4371(98)00549-4

Reaction-diffusion-branching models of stock price fluctuations

Lei Han Tang^*
, Guang Shan Tian

^*Corresponding author for this work

Department of Physics

Research output: Contribution to journal › Journal article › peer-review

26 Citations (Scopus)

Abstract

Several models of stock trading (Bak et al., Physica A 246 (1997) 430.) are analyzed in analogy with one-dimensional, two-species reaction-diffusion-branching processes. Using heuristic and scaling arguments, we show that the short-time market price variation is subdiffusive with a Hurst exponent H=1/4. Biased diffusion towards the market price and blind-eyed copying lead to crossovers to the empirically observed random-walk behavior (H=1/2) at long times. The calculated crossover forms and diffusion constants are shown to agree well with simulation data.

Original language	English
Pages (from-to)	543-550
Number of pages	8
Journal	Physica A: Statistical Mechanics and its Applications
Volume	264
Issue number	3-4
DOIs	https://doi.org/10.1016/S0378-4371(98)00549-4
Publication status	Published - 1 Mar 1999

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02.50.-r
05.40.+j
64.60.Ht
82.20.-w

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abstract = "Several models of stock trading (Bak et al., Physica A 246 (1997) 430.) are analyzed in analogy with one-dimensional, two-species reaction-diffusion-branching processes. Using heuristic and scaling arguments, we show that the short-time market price variation is subdiffusive with a Hurst exponent H=1/4. Biased diffusion towards the market price and blind-eyed copying lead to crossovers to the empirically observed random-walk behavior (H=1/2) at long times. The calculated crossover forms and diffusion constants are shown to agree well with simulation data.",

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note = "Funding Information: One of us (G.S.T) would like to thank the Croucher Foundation for financial support and the Physics Department, Hong Kong Baptist University for their hospitality.",

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AU - Tian, Guang Shan

N1 - Funding Information: One of us (G.S.T) would like to thank the Croucher Foundation for financial support and the Physics Department, Hong Kong Baptist University for their hospitality.

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Y1 - 1999/3/1

N2 - Several models of stock trading (Bak et al., Physica A 246 (1997) 430.) are analyzed in analogy with one-dimensional, two-species reaction-diffusion-branching processes. Using heuristic and scaling arguments, we show that the short-time market price variation is subdiffusive with a Hurst exponent H=1/4. Biased diffusion towards the market price and blind-eyed copying lead to crossovers to the empirically observed random-walk behavior (H=1/2) at long times. The calculated crossover forms and diffusion constants are shown to agree well with simulation data.

AB - Several models of stock trading (Bak et al., Physica A 246 (1997) 430.) are analyzed in analogy with one-dimensional, two-species reaction-diffusion-branching processes. Using heuristic and scaling arguments, we show that the short-time market price variation is subdiffusive with a Hurst exponent H=1/4. Biased diffusion towards the market price and blind-eyed copying lead to crossovers to the empirically observed random-walk behavior (H=1/2) at long times. The calculated crossover forms and diffusion constants are shown to agree well with simulation data.

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Reaction-diffusion-branching models of stock price fluctuations

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