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首页> 外文期刊>Zeitschrift fur Physik, B. Condensed Matter >A Langevin approach to stock market fluctuations and crashes
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A Langevin approach to stock market fluctuations and crashes

机译：用Langevin方法应对股市波动和崩溃

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We propose a non linear Langevin equation as a model for stock market fluctuations and crashes. This equation is based on an identification of the different processes influencing the demand and supply and their mathematical transcription. We emphasize the importance of feedback effects of price variations onto themselves. Risk aversion, in particular, leads to an "up-down" symmetry breaking term which is responsible for crashes, where "panic" is self reinforcing. It is also responsible for the sudden collapse of speculative bubbles. Interestingly, these crashes appear as rare, "activated" events, and have an exponentially small probability of occurence. The model leads to a specific "shape" of the falldown of the price during a crash, which we compare with the October 1987 data. The normal regime, where the stock price exhibits behavior similar to that of a random walk, however reveals non trivial correlations on different time scales, in particular on the time scale over which operators perceive a change of trend.
机译：我们提出了一个非线性Langevin方程作为股票市场波动和崩溃的模型。该方程式基于对影响需求和供应的不同过程及其数学记录的识别。我们强调价格变化对自身的反馈影响的重要性。尤其是风险规避导致“向上-向下”对称破坏术语，该术语负责崩溃，其中“恐慌”是自我强化的。它也是投机泡沫突然崩溃的原因。有趣的是，这些崩溃显示为罕见的“激活”事件，并且发生的可能性很小。该模型导致崩溃期间价格下跌的特定“形状”，我​​们将其与1987年10月的数据进行比较。正常状态下，股票价格表现出与随机游走相似的行为，但是在不同的时间尺度上，特别是在操作员感知趋势变化的时间尺度上，显示出不平凡的相关性。

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