Structural and temporal patterns of the first global trading market

Ribeiro, Ana Sofia; Pinheiro, Flávio L.; Santos, Francisco C.; Polónia, Amélia; Pacheco, Jorge M.

doi:10.1098/rsos.180577

Cited by 4 publications

(3 citation statements)

References 27 publications

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“…Western popular music markets present power law distributions in the lifetime of albums [50]. Stock markets exhibited power law distributions since their very beginning [51]. It has been shown that the number of trades per day, the size of price movements when a large volume of shares are bought or sold, and the number of shares traded per time period are power law distributed with exponents 3, 0.5 and 1.5, respectively [52][53][54].…”

Section: Discussionmentioning

confidence: 99%

A master equation for power laws

Roman

Bertolotti²

2022

R. Soc. open sci.

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We propose a new mechanism for generating power laws. Starting from a random walk, we first outline a simple derivation of the Fokker–Planck equation. By analogy, starting from a certain Markov chain, we derive a master equation for power laws that describes how the number of cascades changes over time (cascades are consecutive transitions that end when the initial state is reached). The partial differential equation has a closed form solution which gives an explicit dependence of the number of cascades on their size and on time. Furthermore, the power law solution has a natural cut-off, a feature often seen in empirical data. This is due to the finite size a cascade can have in a finite time horizon. The derivation of the equation provides a justification for an exponent equal to 2, which agrees well with several empirical distributions, including Richardson’s Law on the size and frequency of deadly conflicts. Nevertheless, the equation can be solved for any exponent value. In addition, we propose an urn model where the number of consecutive ball extractions follows a power law. In all cases, the power law is manifest over the entire range of cascade sizes, as shown through log–log plots in the frequency and rank distributions.

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Section: Discussionmentioning

confidence: 99%

A master equation for power laws

Roman

Bertolotti²

2022

R. Soc. open sci.

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“…Western popular music markets present power law distributions in the lifetime of albums [44]. Stock markets exhibited power law distributions since their very beginning [45]. It has been shown that the number of trades per day, the size of price movements when a large volume of shares are bought or sold, and the number of shares traded per time period are power law distributed with exponents 3, 0.5 and 1.5, respectively [46][47][48].…”

Section: Discussionmentioning

confidence: 99%

A Master Equation for Power Laws

Roman¹,

Bertolotti²

2022

Preprint

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We propose a new mechanism for generating power laws. Starting from a random walk, we first outline a simple derivation of the Fokker-Planck equation. By analogy, starting from a certain Markov chain, we derive a master equation for power laws that describes how the number of cascades changes over time (cascades are consecutive transitions that end when the initial state is reached). The partial differential equation has a closed form solution which gives an explicit dependence of the number of cascades on their size and on time. Furthermore, the power law solution has a natural cut-off, a feature often seen in empirical data. This is due to the finite size a cascade can have in a finite time horizon. The derivation of the equation provides a justification for an exponent equal to 2, which agrees well with several empirical distributions, including Richardson's law on the size and frequency of deadly conflicts. Nevertheless, the equation can be solved for any exponent value.In addition, we propose an urn model where the number of consecutive ball extractions follows a power law. In all cases, the power law is manifest over the entire range of cascade sizes, as shown through log-log plots in the frequency and rank distributions.

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“…Therefore, such system develops relevant norms and institutions to protect them, in the first place, such as the securities market. Then there is the shift of the priority of legislation and other institutions from delegating only the right to possess the means of concomitant production to the delegation of right of use when the owners only financially involved into the enterprise, rarely making significant decisions about it [26][27][28]. Herewith, maritime trading was among the first industries made this transition, switching to the delegation of the right of use by ship owners.…”

Section: Ownershipmentioning

confidence: 99%

Social Systems: Structure, Development and Application of the Fibonacci Sequence

Brazhnikov¹

2021

ECO

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This article presents description of social structures such as, for example, states, in the context of their consideration as systems. Moreover, it seeks to develop K. Marx's model in terms of systematic approach, as well as to justify the application of the Fibonacci sequence to systems in general and, in particular, to social systems. The description covers a wide range of issues, ranging from the assertion of the basic principle of living systems as patterns in resources flows to description of functions of various aspects of states and their economics in terms of objective needs of such structures. In addition, this article justifies synergetic effect based on proposed model, and the way this effect is applied to state systems. Moreover, it includes the description of main changes of socio-economic formations throughout the history as a natural development of social systems, including possible modern stages. The fundamental tool of this description is description of essence of the mechanism of property rights and its formation options. The differences of two extreme directions of such development are also described on the basis of the objective factor of resource provision. Special attention is given to the concept of surplus value as a feature of social production systems.

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Structural and temporal patterns of the first global trading market

Cited by 4 publications

References 27 publications

A master equation for power laws

A master equation for power laws

A Master Equation for Power Laws

Social Systems: Structure, Development and Application of the Fibonacci Sequence

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