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Seven states of randomness

generalization of the idea of randomness

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Record originEnglish Wikipedia
Text licenseCC BY-SA 4.0
Source revisionMay 24, 2025
Entity authorityQ7457565 ↗
Source-derived summary

The seven states of randomness in probability theory, fractals and risk analysis are extensions of the concept of randomness as modeled by the normal distribution. These seven states were first introduced by Benoît Mandelbrot in his 1997 book Fractals and Scaling in Finance, which applied fractal analysis to the study of risk and randomness. This classification builds upon the three main states of randomness: mild, slow, and wild.

The importance of seven states of randomness classification for mathematical finance is that methods such as Markowitz mean variance portfolio and Black–Scholes model may be invalidated as the tails of the distribution of returns are fattened: the former relies on finite standard deviation (volatility) and stability of correlation, while the latter is constructed upon Brownian motion.

History

These seven states build on earlier work of Mandelbrot in 1963: "The variations of certain speculative prices" and "New methods in statistical economics" in which he argued that most statistical models approached only a first stage of dealing with indeterminism in science, and that they ignored many aspects of real world turbulence, in particular, most cases of financial modeling. This was then presented by Mandelbrot in the International Congress for Logic (1964) in an address titled "The Epistemology of Chance in Certain Newer Sciences"

Intuitively speaking, Mandelbrot argued that the traditional normal distribution does not properly capture empirical and "real world" distributions and there are other forms of randomness that can be used to model extreme changes in risk and randomness. He observed that randomness can become quite "wild" if the requirements regarding finite mean and variance are abandoned. Wild randomness corresponds to situations in which a single observation, or a particular outcome can impact the total in a very disproportionate way.

The classification was formally introduced in his 1997 book Fractals and Scaling in Finance, as a way to bring insight into the three main states of randomness: mild, slow, and wild. Given N addends, portioning concerns the relative contribution of the addends to their sum.

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The public source identifies “Seven states of randomness” as generalization of the idea of randomness. This brief keeps that definition visible, then builds a research path around Seven, states and randomness.

Editorial reviewA concise reference frame for defining the subject, testing terminology and identifying the institution closest to the evidence. The current lead gives the account dated anchors—1997, 1963, 1964—that can be checked directly. The selected authority fields contribute no independent date. Its value is orientation rather than verdict, with Seven, states and randomness providing the first useful test.
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This entry incorporates text from “Seven states of randomness” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.