金融市场与物理世界存在一定的联系,证券价格波动表现出一定的粒子行为特征.首先,对量子物理中的方势阱进行总结,并将其延伸到更具一般意义、更复杂的势阱上.然后,通过MATLAB求解超越方程,得出波函数的数值解,并做出其几率分布图像.最后,用一维非对称有限深方势阱拟合上证指数收益率.研究发现,波函数几率分布对指数收益率具有较好的拟合作用,指数波动具有丰富的物理内涵.研究丰富了金融物理学相关成果,且对市场建设、风险管理等有重要启示.
Abstract
There are some certain relationships between the financial market and the physical world. The fluctuation of security price shows a certain characteristic of particle behavior. Firstly, we summarize the square potential well in quantum physics, and extend the objective law to more general and complex ones. Then we solve the transcendental equation by MATLAB, and deduce the numerical solution of the wave function and its probability distribution image. Lastly, we use one dimensional unsymmetrical finite deep square potential well to fit the rate of return of Shanghai Stock Index. We find that the fitting effect is satisfactory, and the volatility of Stock Index has some rich physical connotations. This research could enrich the results of Econophysics, and has important enlightenment to capital market construction and risk management.
关键词
金融物理 /
一维非对称有限深方势阱 /
波函数 /
上证指数
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Key words
econophysics /
one dimensional unsymmetrical finite deep square potential well /
wave function /
Shanghai Stock Index
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参考文献
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脚注
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基金
广东省自然科学基金资助项目(2017A030313420);广东省哲学社会科学基金资助项目(GD14XYJ16);广东省教育厅人文社科基金资助项目(2014WQNCX074)
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