### On Crises in Financial Markets

#### Abstract

The reasons of the financial markets collapse and methods of their forecasting are investigated in this article. A model based on hypothesis of the quantum nature of the impact of information on financial markets is given. It is shown that in information-saturated volatile financial markets, sharp price jumps are really expected

Motivation for this research is inability of traditional approach for explaining sharp price jumps during financial crises. They are unexpected according to the traditional theories. When considering the logarithm of relative price changes over the period *y _{tk}* = ln(

*N*/

_{tk}*N*

_{tk}_{-1}) it was found that the statistical characteristics of this random value differ from the characteristics of the normal distribution. The approach, developed in this paper, explaining the possibility of sharp price jumps, seems to be more harmonious than the traditional approach.

Novelty of given approach consists in considering a model based on the assumption about the quantum (discontinuous) nature of information impact on financial markets. The process of information transfer is quantum – i. e. the information is transmitted in portions, multiples of a quantum of information. There are discrete information levels. When moving from one level to another, it is necessary to absorb or emit one quantum of information. Thus, the amount of information of a particular level is necessarily a multiple of the quantum of information.

Methodology and methods are based on probability and differential equations. Equation with respect to logarithm of increment of prices *y* = ln(*N*(*t*_{0}+D*t*)/*N*(*t*_{0})) is thoroughly investigated. The probability density function for each information price level *P _{n}*(

*y*) = Y

^{2}

*(*

_{n}*y*), where Y(

*y*) is called the wave function of prices. Equation with respect to Y(

*y*) is thoroughly investigated too.

There are many calculations of various probabilities and other characteristics of *y* (logarithm of prices increment) for different information price level. The hierarchy of information-price levels is autonomous – i.e. each of them has its own separate probability characteristics, different functions of probability density distribution. The normal distribution takes place only when n=0. For all others n=1, 2, 3... the density functions are different from Gaussian.

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ISSN: 1929-7092