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International Journal of Mathematics and Mathematical Sciences

Asymmetric Information and Quantization in Financial Economics

Raymond J. Hawkins, B. Roy Frieden

Published Jan 1, 2012• 13 citations
Publisher

Abstract

We show how a quantum formulation of financial economics can be derived from asymmetries with respect to Fisher information. Our approach leverages statistical derivations of quantum mechanics which provide a natural basis for interpreting quantum formulations of social sciences generally and of economics in particular. We illustrate the utility of this approach by deriving arbitrage-free derivative-security dynamics.

DOI
10.1155/2012/470293

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We show how a quantum formulation of financial economics can be derived from asymmetries with respect to Fisher information. Our approach leverages statistical derivations of quantum mechanics which provide a natural basis for interpreting quantum formulations of social sciences generally and of economics in particular. We illustrate the utility of this approach by deriving arbitrage-free derivative-security dynamics.
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.
In this talk we intend to provide for an overview of the uses we can make in financial economics of several quantum physical concepts. We introduce and briefly discuss the so called information wave function. We discuss how the information wave function can be of use in financial option pricing. We then briefly allude on how the information wave function can be used in arbitrage. We briefly discuss how the information wave concept can be connected to measures of information. We round off the paper on recent work we are doing with Andrei Khrennikov on i) testing probability interference in psychology (Khrennikov and Haven 2006 (I)) and ii) finding uses of ‘financial ’ nonlocality and entanglement (Khrennikov and Haven 2006 (II)). In summary this talk addresses interference (probability interference), financial entanglement and looks at using the wave function in a variety of ways within an economics/finance – political science – social interaction environment.
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Written by world experts in the foundations of quantum mechanics and its applications to social science, this book shows how elementary quantum mechanical principles can be applied to decision-making paradoxes in psychology and used in modelling information in finance and economics. The book starts with a thorough overview of some of the salient differences between classical, statistical and quantum mechanics. It presents arguments on why quantum mechanics can be applied outside of physics and defines quantum social science. The issue of the existence of quantum probabilistic effects in psychology, economics and finance is addressed and basic questions and answers are provided. Aimed at researchers in economics and psychology, as well as physics, basic mathematical preliminaries and elementary concepts from quantum mechanics are defined in a self-contained way.
The relationship between expectation and price is commonly established with two principles: no-arbitrage, which asserts that both maps are positive; and equivalence, which asserts that the maps share the same null events. Constructed from the Arrow-Debreu securities, classical and quantum models of economics are then distinguished by their respective use of classical and quantum logic, following the program of von Neumann. In this essay, the operations and axioms of quantum groups are discovered in the minimal preconditions of stochastic and functional calculus, making this the natural domain for the axiomatic development of mathematical finance. Quantum economics emerges from the twin pillars of the Gelfand-Naimark-Segal construction, implementing the principle of no-arbitrage, and the Radon-Nikodym theorem, implementing the principle of equivalence. Exploiting quantum group duality, a holographic principle that exchanges the roles of state and observable creates two distinct economic models from the same set of elementary valuations. Advocating on the grounds that this contains and extends classical economics, noncommutativity is presented as a modelling resource, with novel applications in the pricing of options and other derivative securities.