Predicting Financial Contagion and Crisis by Using Jones, Alexander Polynomial and Knot Theory

Topological methods are rapidly developing and are becoming more used in physics, biology and chemistry. One area of topology has showed its immense potential in explaining potential financial contagion and financial crisis in financial markets. The aforementioned method is knot theory. The movement of stock price has been marked and braids and knots have been noted. By analysing the knots and braids using Jones polynomial, it is tried to find if there exists an untrivial knot equal to unknot? After thorough analysis, possible financial contagion and financial crisis prediction are analysed by using instruments of knot theory pertaining in that sense to Jones, Laurent and Alexander polynomial. It is proved that it is possible to predict financial disruptions by observing possible knots in the graphs and finding appropriate polynomials. In order to analyse knot formation, the following approach is used: “Knot formation in three-dimensional space is considered and the equations about knot forming and its disentangling are considered”. After having defined the equations in three-dimensional space, the definition of Brownian bridge concerning formation of knots in three-dimensional space is defined. Using analogy method, the notion of Brownian bridge is translated into 2-dimensional space and the foundations for the application of knot theory in 2-dimensional space have been set up. At the same time, the aforementioned approach is innovative and it could be used in accordance with stochastic analysis and quantum finance.

来源: Predicting Financial Contagion and Crisis by Using Jones, Alexander Polynomial and Knot Theory

Advertisements

发表评论

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / 更改 )

Twitter picture

You are commenting using your Twitter account. Log Out / 更改 )

Facebook photo

You are commenting using your Facebook account. Log Out / 更改 )

Google+ photo

You are commenting using your Google+ account. Log Out / 更改 )

Connecting to %s