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150325s1998 xx |||||o 00| ||eng c |
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|a (DE-627)JST07037600X
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|a (JST)44612
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|a DE-627
|b ger
|c DE-627
|e rakwb
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|a eng
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|a Segal, Wiliam
|e verfasserin
|4 aut
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|a The Black-Scholes Pricing Formula in the Quantum Context
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|c 1998
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|a Text
|b txt
|2 rdacontent
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|a Computermedien
|b c
|2 rdamedia
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|a Online-Ressource
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|a A natural explanation for extreme irregularities in the evolution of prices in financial markets is provided by quantum effects. The lack of simultaneous observability of relevant variables and the interference of attempted observation with the values of these variables represent such effects. These characteristics have been noted by traders and economists and appear intrinsic to market dynamics. This explanation is explored here in terms of a corresponding generalization of the Wiener process and its role in the Black-Scholes-Merton theory. The differentiability of the Wiener process as a sesquilinear form on a dense domain in the Hilbert space of square-integrable functions over Wiener space is shown and is extended to the quantum context. This provides a basis for a corresponding generalization of the Ito theory of stochastic integration. An extension of the Black-Scholes option pricing formula to the quantum context is deduced.
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|a Copyright 1993-1998 National Academy of Sciences
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|a Economic Sciences
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|a Brownian motion
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|a Quantum process
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|a Stochastic integration
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|a Ito lemma
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|a Black-Scholes-Merton theory
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|a Mathematics
|x Mathematical expressions
|x Mathematical functions
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|a Mathematics
|x Pure mathematics
|x Probability theory
|x Random variables
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|a Mathematics
|x Pure mathematics
|x Linear algebra
|x Vector analysis
|x Mathematical vectors
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|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Statistical physics
|x Dimensional analysis
|x Dimensionality
|x Abstract spaces
|x Topological spaces
|x Metric spaces
|x Separable spaces
|x Banach space
|x Hilbert spaces
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|a Mathematics
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|a Physical sciences
|x Physics
|x Microphysics
|x Quantum mechanics
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|a Mathematics
|x Pure mathematics
|x Probability theory
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|a Mathematics
|x Pure mathematics
|x Calculus
|x Differential calculus
|x Mathematical integration
|x Mathematical integrals
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|a Economics
|x Economic disciplines
|x Financial economics
|x Financial markets
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|a Information science
|x Public information
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|a research-article
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|a Segal, I. E.
|e verfasserin
|4 aut
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|i Enthalten in
|t Proceedings of the National Academy of Sciences of the United States of America
|d National Academy of Sciences of the United States of America
|g 95(1998), 7, Seite 4072-4075
|w (DE-627)254235379
|w (DE-600)1461794-8
|x 10916490
|7 nnns
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|g volume:95
|g year:1998
|g number:7
|g pages:4072-4075
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|u https://www.jstor.org/stable/44612
|3 Volltext
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|d 95
|j 1998
|e 7
|h 4072-4075
|