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Palgrave Macmillan UK eBooks

Quantization in Financial Economics: An Information-Theoretic Approach

Raymond J. Hawkins, B. Roy Frieden

Published Jan 1, 2017• 5 citations
Publisher

Abstract

The authors show how the formal framework of quantum mechanics arises in economics generally and in financial economics in particular as a natural consequence of an information-theoretic approach to these fields. Specifically, extremizing Fisher information, subject to the constraint that the associated probability density reproduces observed economic phenomena, results in Schrödinger-like equations. The authors illustrate the utility of this approach with examples from financial economics. As an emergent consequence of information theory, the use of quantum formalism in economics can be seen as a powerful approach for understanding complex dynamics grounded in the probabilistic view of economics advocated by Knight and Keynes. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

DOI
10.1057/978-1-137-49276-0_2

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The authors show how the formal framework of quantum mechanics arises in economics generally and in financial economics in particular as a natural consequence of an information-theoretic approach to these fields. Specifically, extremizing Fisher information, subject to the constraint that the associated probability density reproduces observed economic phenomena, results in Schrödinger-like equations. The authors illustrate the utility of this approach with examples from financial economics. As an emergent consequence of information theory, the use of quantum formalism in economics can be seen as a powerful approach for understanding complex dynamics grounded in the probabilistic view of economics advocated by Knight and Keynes. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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This article explores the interdisciplinary interface between quantum computing and economic theory, with a particular emphasis on how foundational concepts from quantum mechanics reshape core methodological and epistemological assumptions in economics. Drawing on a comprehensive bibliographic methodology, the study synthesizes contributions from quantum physics, computational theory, and economic modeling to trace the impact of quantum logic -especially principles such as superposition, entanglement, and measurement irreversibility- on both theoretical constructs and applied frameworks. Particular attention is given to emblematic algorithms (e.g., Shor’s and Grover’s) as case studies for illustrating computational discontinuities in fields such as cryptographic trust, portfolio optimization, and decision-making under uncertainty. The article also surveys recent developments in quantum machine learning and quantum-inspired models relevant to economic forecasting and adaptive policy design. Ethical and distributional concerns are critically addressed, especially in relation to the asymmetric global access to quantum resources. By mapping this emerging field through a structured review of cross-disciplinary literature, the paper offers a conceptual framework for understanding how quantum technologies may influence future research in financial economics, risk theory, and the modeling of complex systems operating under deep informational constraints.
This work presents a reconstruction of quantum mechanics in which Schrödinger-type dynamics emerges from reversible probabilistic evolution rather than being postulated. Starting from a normalized probability density, we impose reversible probability dynamics, Fisher information geometry, and classical correspondence. These compatibility conditions yield coupled real equations equivalent to the continuity equation and the Hamilton–Jacobi equation with an additional information curvature (quantum potential) term. By combining density and phase into a complex amplitude, the Schrödinger equation appears as a compact encoding of reversible statistical flow. The result is mathematically equivalent to the Madelung hydrodynamic formulation and structurally connected to Bohmian mechanics, but derived without assuming Hilbert space, operator axioms, or measurement postulates. The work can therefore be viewed as an information-geometric derivation of quantum dynamics: quantum theory arises as the unique consistent representation of reversible probability flow. Keywords: quantum foundations, quantum reconstruction, emergent quantum mechanics, derivation of the Schrödinger equation, information geometry, Fisher information, Hamilton–Jacobi theory, Madelung formulation, Bohmian mechanics, reversible probability dynamics
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The situation in probability theory is more or less analogous to the situation in geometry in the 19th century. Many scientists begin to understand that the Kol-mogorov axiomatic approach [1], 1933, to the modern theory of probability cannot describe all probabilistic phenomena observed in nature. Hence, the theory of probability based on this axiomatic approach is not a unique and universal probabilistic formalism. It is only one model, namely, the Kolmogorov probabilistic model. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.