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. 1. Introduction Asymmetric information lies at the heart of capital markets and how it induces information flow and economic dynamics is a key element to understanding the structure and function of economic systems generally and of price discovery in particular [1–3]. The information-theoretic underpinnings of economics also provide a common framework through which economics can leverage results in other fields, an example being the well-known use of statistical mechanics in financial economics (see, e.g., [44, 45] and references therein). In addition to the statistical-mechanics representation of financial economics, however, a quantum-mechanics representation has also emerged (see [5, 18–30, 42, 46–48]) and the purpose of this paper is to show that this quantum framework too can be derived from asymmetric information, thus providing a more comprehensive information-theoretic basis for financial economics. Financial economics is unique among economic disciplines in the extent to which stochastic processes are employed as an explanatory framework, a ubiquity epitomized in the modeling of financial derivatives.1 Building on a history of shared metaphor between classical physics and neoclassical economics [4] and the initial use of simple diffusion processes, financial economics and statistical mechanics found a common language in stochastic dynamics with which statistical mechanics could be applied across a wide range of economics including finance, macroeconomics, and risk management (see, e.g., [44, 45, 52–56]). Underlying that common language is a fundamental information-theoretic basis, a basis with which financial economics can be expressed as probability theory with constraints.2 It is from the perspective of financial economics as probability theory with constraints that we propose to show how and why financial economics can be expressed as a quantum theory. Financial economics as quantum theory has developed in a manner similar to that taken by statistical mechanics, exploiting formal similarities (see [5, 18–30, 42, 46–48]). Financial economics as a quantum theory, however, lacks the history of common metaphor that enabled
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The information-theoretic basis of statistical mechanics is discussed in [57–61]. The relationship between information theory and economics is discussed in detail in [11] and references therein. In recent communications we have shown that the dynamics of economic systems can be derived from information asymmetry with respect to Fisher information and that this form of asymmetric information yields a powerful explanatory statistical mechanical framework for financial economics [10–15]. With a common information-theoretic basis for both statistical mechanics and financial economics the notion of statistical mechanics as probability theory with constraints (see, e.g., [62]) suggests that financial economics can be expressed as probability theory with constraints.
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