Frezza Massimiliano
Department of Economics and Law, University of Cassino and Southern Lazio (UCLAM), Cassino 03043, Italy.
Chaos. 2018 Sep;28(9):091102. doi: 10.1063/1.5050867.
The recent global financial crisis has threatened the financial system with total collapse of many economic sectors with a particular penetration to world's stock markets. The large swings in the prices of international stocks or indexes have reinvigorated the debate on their mathematical modeling. The traditional approaches do not seem to be very exhaustive and satisfactory, especially when extreme events occur. We propose a fractal-based approach to model the actual prices by assuming that they follow a Multifractional Process with Random Exponent. An empirical evidence is offered that this stochastic process is able to provide an appropriate modeling of actual series in terms of goodness of fit by comparing three main stock indexes.
最近的全球金融危机使金融系统面临许多经济部门全面崩溃的威胁，对全球股票市场的影响尤为显著。国际股票价格或指数的大幅波动重新引发了对其数学建模的争论。传统方法似乎并不十分详尽和令人满意，尤其是在极端事件发生时。我们提出一种基于分形的方法来对实际价格进行建模，假设它们遵循具有随机指数的多重分形过程。通过比较三个主要股票指数，提供了经验证据，表明这个随机过程能够在拟合优度方面为实际序列提供适当的建模。
