【作者】 周石鹏； 肖柳青；

【Author】 Shipeng Zhou~1 Liuqing Xiao~2 1 Business School,Shanghai University for Science and Technology,China 200093 2 Department of Mathematics,Shanghai Jiao Tong University,China 200240

【机构】 上海理工大学管理学院； 上海交通大学理学院数学系；

【摘要】 本文是应用物理中规范场理论的规范对称性思想和分析方法来研究了金融产品的价格动态规律对于任意计价单位变换的不变性—规范对称性,并以此来讨论资产组合价值的动态行为.我们的研究表明在金融市场系统中这种规范对称性有着合理的几何解释:它能在几何框架中定义出联络(规范势)和相应的协变导数,使得该联络的曲率与金融市场上的套利之间存在着直接的联系,即,当且仅当曲率为零时市场是无套利的.这种对称性研究方法为人们揭示和解释了金融市场的基本假设与所隐含的动态规律之间的某种隐含的关系.更多还原

【Abstract】 In this paper,we study invariance—gauge symmetry in the dynamics of the prices of financial products under any transformation of numeraire by means of the approach and idea of the symmetrical analysis in the gauge field theory in Physics.And the dynamic behavior of portfolio value is discussed.Our research shows that this gauge symmetry in financial market has a reasonable geometrical interpretation:it can determine a relevant connection(gauge potential) such that there is a close relationship between the curvature and arbitrage in financial market,i.e.there is no arbitrage in financial market if and only if the curvature of the connection is zero.This symmetrical approach could reveal and understand some hidden relationship between the fundamental hypotheses and the dynamic laws of prices in financial market.更多还原