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Fluctuations of interface statistical physics models applied to a stock market model. (English) Zbl 1134.91468

Summary: Applying the theory of fluctuations of the interfaces for statistical physics lattice models, we construct a financial model and use this financial model to describe the behavior or fluctuations of a stock price process in a stock market. By using the methods of statistical physics and under some conditions, we show that the finite dimensional distribution of a normalized random process for this financial model converges to the corresponding distribution of the Black-Scholes model.

MSC:

91B80 Applications of statistical and quantum mechanics to economics (econophysics)
91G80 Financial applications of other theories
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