Solitary wave solutions of nonlinear financial markets :data-modeling-concept-practicing |
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Authors: | Ma Jin-long and MA Fei-te |
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Affiliation: | (1) Guangzhou Institute of Geochemistry, Chinese Academy of Sciences, Guangzhou, 510640, China;(2) Changsha Workroom of Nonlinear Special Dynamics, Changsha, 410013, China;(3) Changsha Workroom of Nonlinear Special Dynamics, Changsha, 410013, China |
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Abstract: | This paper seeks to solve the difficult nonlinear problem in financial markets on the complex system theory and the nonlinear
dynamics principle, with the data-model-concept-practice issue-oriented reconstruction of the phase space by the high frequency
trade data. In theory, we have achieved the differentiable manifold geometry configuration, discovered the Yang-Mills functional
in financial markets, obtained a meaningful conserved quantity through corresponding space-time non-Abel localization gauge
symmetry transformation, and derived the financial solitons, which shows that there is a strict symmetry between manifold
fiber bundle and guage field in financial markets. In practical applications of financial markets, we have repeatedly carried
out experimental tests in a fluctuant evolvement, directly simulating and validating the existence of solitons by researching
the price fluctuations (society phenomena) using the same methods and criterion as in natural science and in actual trade
to test the stock Guangzhou Proprietary and the futures Fuel Oil in China. The results demonstrate that the financial solitons
discovered indicates that there is a kind of new substance and form of energy existing in financial trade markets, which likely
indicates a new science paradigm in the economy and society domains beyond physics.
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Keywords: | noneuclidean geometry manifold nonlinear finance market solitary wave price fluctuation data mining gauge modeling financial soliton |
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