Pilot-Wave Theory and Financial Option Pricing

Haven, Emmanuel

doi:10.1007/s10773-005-8973-3

Cited by 51 publications

(53 citation statements)

References 7 publications

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“…So far, the application of quantum structures has been focused mainly on economics [38,39,40,41], psychology and cognition, concepts theories and decision theory [26,30,31,24,25,42], and language, information retrieval and artificial intelligence [43,44,45,33,46,47,34].…”

Section: Resultsmentioning

confidence: 99%

"Квантовая" Теория Принятия Решений В Политической Науке

Алексеева¹,

Минеев²,

Loshkariov³

2017

Полис

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We elaborate a theory for the modeling of concepts using the mathematical structure of quantum mechanics. Concepts are represented by vectors in the complex Hilbert space of quantum mechanics and membership weights of items are modeled by quantum weights calculated following the quantum rules. We apply this theory to model the disjunction of concepts and show that experimental data of membership weights of items with respect to the disjunction of concepts can be modeled accurately. It is the quantum effects of interference and superposition, combined with an effect of context, that are at the origin of the effects of overextension and underextension observed as deviations from a classical use of the disjunction. We put forward a graphical explanation of the effects of overextension and underextension by interpreting the quantum model applied to the modeling of the disjunction of concepts.

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Section: Resultsmentioning

confidence: 99%

"Квантовая" Теория Принятия Решений В Политической Науке

Алексеева¹,

Минеев²,

Loshkariov³

2017

Полис

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“…The problem created by unrecognizability of the Fibonacci states subset E F in a finite time might still be important to the application of quantum formalism to so-called quantum-like systems, i.e., non-physical systems ranging, for example, from finance [15,16] and population dynamics [17] to social science [18], psychology [19], cognition [20] and neuroscience [21].…”

Section: Fibonacci Numbers Have No Physical Relevancementioning

confidence: 99%

Effectively Calculable Quantum Mechanics

Bolotin

2016

PSIJ

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According to mathematical constructivism, a mathematical object can exist only if there is a way to compute (or "construct") it; so, what is non-computable is non-constructive. In the example of the quantum model, whose Fock states are associated with Fibonacci numbers, this paper shows that the mathematical formalism of quantum mechanics is non-constructive since it permits an undecidable (or effectively impossible) subset of Hilbert space. On the other hand, as it is argued in the paper, if one believes that testability of predictions is the most fundamental property of any physical theory, one need to accept that quantum mechanics must be an effectively calculable (and thus mathematically constructive) theory. With that, a way to reformulate quantum mechanics constructively, while keeping its mathematical foundation unchanged, leads to hypercomputation. In contrast, the proposed in the paper superselection rule, which acts by effectively forbidding a coherent superposition of quantum states corresponding to potential and actual infinity, can introduce computable constructivism in a quantum mechanical theory with no need for hypercomputation.

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“…There have been applications of pilot wave theory to finance. See Khrennikov [5,6]; Choustova [19]; Haven and Khrennikov [20] and Haven [21]. An important element in this approach to finance is that borrowing from pilot-wave theory allows for a formalism, which we could call, information dynamics.…”

Section: Introductionmentioning

confidence: 99%

Using Empirical Data to Estimate Potential Functions in Commodity Markets: Some Initial Results

Shen

Haven

2017

Int J Theor Phys

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This paper focuses on estimating real and quantum potentials from financial commodities. The log returns of six common commodities are considered. We find that some phenomena, such as the vertical potential walls and the time scale issue of the variation on returns, also exists in commodity markets. By comparing the quantum and classical potentials, we attempt to demonstrate that the information within these two types of potentials is different. We believe this empirical result is consistent with the theoretical assumption that quantum potentials (when embedded into social science contexts) may contain some social cognitive or market psychological information, while classical potentials mainly reflect 'hard' market conditions. We also compare the two potential forces and explore their relationship by simply estimating the Pearson correlation between them. The Medium or weak interaction effect may indicate that the cognitive system among traders may be affected by those 'hard' market conditions.

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Pilot-Wave Theory and Financial Option Pricing

Cited by 51 publications

References 7 publications

"Квантовая" Теория Принятия Решений В Политической Науке

"Квантовая" Теория Принятия Решений В Политической Науке

Effectively Calculable Quantum Mechanics

Using Empirical Data to Estimate Potential Functions in Commodity Markets: Some Initial Results

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