One of the objections often leveled at the approach of physicists working with economic systems is that this kind of activity cannot be a branch of physics because the ‘equation of motion of the process’ is unknown. But if this criterion – requiring that the Hamiltonian of the process be known or obtainable – were to be applied across the board, several fruitful current research fields in physics would be disqualified, e.g., the modeling of friction and many studies in the area of granular matter. Moreover, a number of problems in physics that are described by a well defined equation – such as turbulence [61] – are not analytically solvable, even with sophisticated mathematical and physical tools.

On a qualitative level, turbulence and financial markets are attractively similar. For example, in turbulence, one injects energy at a large scale by, e.g., stirring a bucket of water, and then one observes the manner in which the energy is transferred to successively smaller scales. In financial systems ‘information’ can be injected into the system on a large scale and the reaction to this information is transferred to smaller scales – down to individual investors. Indeed, the word ‘turbulent’ has come into common parlance since price fluctuations in finance qualitatively resemble velocity fluctuations in turbulence. Is this qualitative parallel useful on a quantitative level, such that our understanding of turbulence might be relevant to understanding price fluctuations?

In this chapter, we will discuss fully developed turbulence in parallel with the stochastic modeling of stock prices.