## Mathematical analysis of Soros’s theory of reflexivity (2008)

### BibTeX

@MISC{Kwong08mathematicalanalysis,

author = {C. P. Kwong},

title = {Mathematical analysis of Soros’s theory of reflexivity},

year = {2008}

}

### OpenURL

### Abstract

The mathematical model proposed by George Soros for his theory of reflexivity is analyzed under the framework of discrete dynamical systems. We show the importance of the notion of fixed points for explaining the behavior of a reflexive system governed by its cognitive and manipulative functions. The interrelationship between these two functions induces fixed points with different characteristics, which in turn generate various system behaviors including the so-called “boom then bust ” phenomenon in Soros’s theory. Key words: Soros’s theory of reflexivity, Discrete dynamical systems JEL classifications: B41, C69 1

### Citations

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Citation Context ...these complex social systems as we do for physical or biological systems. The mathematics so used need not be very advanced and abstract to be effective. The works of Nobel Laureates Daniel Kahneman (=-=Kahneman and Tversky, 1979-=-) and Thomas C. Schelling (Schelling, 2006) for modeling human behaviors are two typical examples. It is important to learn from these examples, that in many cases the effectiveness of mathematics in ... |

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Citation Context ... Introduction The theory of reflexivity is a theoretical construct of George Soros’s philosophy on prices in financial markets. The theory was first documented by Soros in his The Alchemy of Finance (=-=Soros, 1987-=-), expanded ∗The Chinese University of Hong Kong, Hong Kong. Address for correspondence: Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Ko... |

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Citation Context ..., (x1, y1), (x2, y2), . . . } the (forward) orbit of (x0, y0) under S. Dynamical systems of this kind have been extensively studied (see, for example, (Hale and Koçak, 1996), 5(Holmgren, 1996), and (=-=Robinson, 2004-=-)) and this is why we claim in the Introduction that Equation (1) is very amenable to mathematical analysis. In the next section we will frequently apply existing results from discrete dynamical syste... |

17 |
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Citation Context ... N.T., Hong Kong; email: cpkwong@mae.cuhk.edu.hk 1in Open Society (Soros, 2000), and reiterated, using the recent credit crisis as example, in his latest work The New Paradigm for Financial Markets (=-=Soros, 2008-=-). From the outset Soros does not believe, that the methods of natural sciences can be applied to the study of social sciences such as economics. Simply put, in his own words, there is no hope to obta... |

13 |
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Citation Context ... Kong. Address for correspondence: Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong; email: cpkwong@mae.cuhk.edu.hk 1in Open Society (=-=Soros, 2000-=-), and reiterated, using the recent credit crisis as example, in his latest work The New Paradigm for Financial Markets (Soros, 2008). From the outset Soros does not believe, that the methods of natur... |

11 |
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Citation Context .... At this junction it may be worthwhile to consider the role of mathematical modeling in studying economics in order to justify our present effort. The topic is big and controversial (Mirowski, 1986; =-=Debreu, 1991-=-; Beed and Kane, 1991; Velupillai, 2005). However, our view is simple (and of course, nonsingular) enough to be expressed within a paragraph. We admit that what social scientists are trying to explore... |

4 |
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(Show Context)
Citation Context ...et of points {(x0, y0), (x1, y1), (x2, y2), . . . } the (forward) orbit of (x0, y0) under S. Dynamical systems of this kind have been extensively studied (see, for example, (Hale and Koçak, 1996), 5(=-=Holmgren, 1996-=-), and (Robinson, 2004)) and this is why we claim in the Introduction that Equation (1) is very amenable to mathematical analysis. In the next section we will frequently apply existing results from di... |

2 | 1989] An Introduction to Chaotic Dynamical Systems, 2nd edition - L |

2 |
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(Show Context)
Citation Context ...′ ( ¯x)| < 1 |φ′ , (6) ( ¯y)| and it is unstable if | f ′ ( ¯x)| > 1 |φ′ . (7) ( ¯y)| Proof. Since f(x) and φ(y) are differentiable, then the composite function Γ = φ ◦ f is also differentiable (see (=-=Gaskill and Narayanaswami, 1998-=-) or other standard texts on calculus). Furthermore, Γ ′ (x) = φ ′ ( f(x)) f ′ (x). (8) A fixed point ¯x of a differentiable function, say our function Γ(x), is asymptotically stable if |Γ ′ ( ¯x)| < ... |

1 |
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Citation Context ...tion it may be worthwhile to consider the role of mathematical modeling in studying economics in order to justify our present effort. The topic is big and controversial (Mirowski, 1986; Debreu, 1991; =-=Beed and Kane, 1991-=-; Velupillai, 2005). However, our view is simple (and of course, nonsingular) enough to be expressed within a paragraph. We admit that what social scientists are trying to explore are systems of extre... |

1 |
Theory of reflexivity by George Soros: attempt of critical analysis
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(Show Context)
Citation Context ...omics, the lack of such an interest is somewhat puzzling since Equation (1) is very amenable to mathematical analysis as we will show in this paper. The article, published by Birshtein and Borsevici (=-=Birshtein and Borsevici, 2002-=-), is perhaps the only exception. There the authors make explicit the recursive nature of Equation (1) and then use graphical analysis to show that equilibria do exist in the reflexive model, a result... |

1 |
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Citation Context ...stance all Soros’s published writings are narrative in nature and neither other representative reviews on the theory of reflexivity have addressed this fundamental equation (Cross and Strachan, 1997; =-=Bryant, 2002-=-). Soros may be excused from the duty of performing the mathematical analysis because he “was not very good at math”. But for other mathematically inclined researchers in finance or economics, the lac... |

1 |
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(Show Context)
Citation Context ... himself or others. For instance all Soros’s published writings are narrative in nature and neither other representative reviews on the theory of reflexivity have addressed this fundamental equation (=-=Cross and Strachan, 1997-=-; Bryant, 2002). Soros may be excused from the duty of performing the mathematical analysis because he “was not very good at math”. But for other mathematically inclined researchers in finance or econ... |

1 |
Mathematical formalism and economic explanation
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(Show Context)
Citation Context ...ose of our study. At this junction it may be worthwhile to consider the role of mathematical modeling in studying economics in order to justify our present effort. The topic is big and controversial (=-=Mirowski, 1986-=-; Debreu, 1991; Beed and Kane, 1991; Velupillai, 2005). However, our view is simple (and of course, nonsingular) enough to be expressed within a paragraph. We admit that what social scientists are try... |