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The Black-Scholes pricing formula in the quantum context.

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The Black-Scholes pricing formula in the quantum context.

Content Provider	World Health Organization (WHO)-Global Index Medicus
Author	Segal, I. E. Segal, W.
Description	Author Affiliation: Segal W ( Office of Policy Development and Research, Department of Housing and Urban Development, 451 7th Street, SW, Room 8212, Washington, DC 20410, USA.);
Abstract	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.
ISSN	00278424
e-ISSN	10916490
Journal	Proceedings of the National Academy of Sciences of the United States of America
Issue Number	7
Volume Number	95
Language	English
Publisher	National Academy of Sciences
Publisher Date	1998-01-01
Publisher Place	United States
Access Restriction	Open
Subject Keyword	Multidisciplinary
Content Type	Text
Resource Type	Article
Subject	Multidisciplinary

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