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**1 - 2**of**2**### Modeling and Optimization of Process Engineering Problems Containing Black-Box Systems and Noise

, 2008

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### A DYNAMICAL APPROACH TO STOCK MARKET FLUCTUATIONS

, 2010

"... The recent turbulence on the world’s stock markets has reinvigorated the attack on classical economic models of stock market fluctuations. The key problem is determining a dynamic model, which is consistent with observed fluctuations and which reflects investor behavior. Here, we use a novel equatio ..."

Abstract
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The recent turbulence on the world’s stock markets has reinvigorated the attack on classical economic models of stock market fluctuations. The key problem is determining a dynamic model, which is consistent with observed fluctuations and which reflects investor behavior. Here, we use a novel equation-free approach developed in nonlinear dynamics literature to identify the salient statistical features of fluctuations of the Dow Jones Industrial Average over the past 80 years. We then develop a minimal dynamical model in the form of a stochastic differential equation involving both additive and multiplicative system-noise couplings, which captures these features and whose parameterization on a time scale of days can be used to capture market distributions up to a time scale of months. The terms in the model can be directly linked to “herding” behavior on the part of traders. However, we show that parameters in this model have changed over a number of decades producing different market regimes. This result partially explains how, during some periods of history, “classic ” economic models may work well and at other periods “econo-physics ” models prove better.