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.

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 [

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}^{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 [^{3}

To this end we continue in Section

It is our view that all things economic are information-theoretic in origin: economies are participatory, observer participancy gives rise to information, and information gives rise to economics. Dynamical laws follow from a perturbation of information flow which arises from the asymmetry between

We consider the price of an asset, liability, or more generally of a security which, for a given instant in time

The classical Fisher information

The intrinsic information

To develop ^{4}

Our second assumption is that a cash-flow price can be represented by a probability distribution

These three assumptions coalesce in the information

The last two of our three assumptions imply that the velocity ^{5}

To minimize the Fisher information

To complete the model we need Lagrange multipliers that are consistent with our information ^{6}

Determining the Lagrange multipliers

A particular advantage of our Fisher information approach to dynamics in financial economics is the natural way by which both time dependence and departures from equilibrium arise. Time dependence of the probability density and, by implication, security prices is expressed in (

Extending this to call and put options which are the partial moments,

From the perspective of information theory, the quantum representation of financial economics is a natural outcome of the process of inference using Fisher information. This approach also complements the work of Haven, Choustova and Khrennikov [^{7}

Quantum theory is an attractive formalism to use in the treatment of economics generally and of financial economics in particular due to the manner in which uncertainty arises [

The authors thank Professor Emmanuel Haven for bringing the use of the de Broglie-Bohm approach in financial economics to our attention through his engaging presentation and our subsequent conversations at the 2011 Winter Workshop on Economic Heterogeneous Interacting Agents held at Tianjin University. The authors thank Professor Ewan Wright for many helpful conversations regarding information theory and the statistical basis of quantum mechanics, and his insight and suggestions that materially improved this paper. The authors also thank Dr. Dana Hobson and Dr. Minder Cheng for insight concerning price momentum.

The physical basis for employing stochastic dynamics, uncertainty, has been a part of economics generally for some time since the pioneering work of Keynes and Knight [

The information-theoretic basis of statistical mechanics is discussed in [

For a review of the statistical origins of quantum mechanics, see [

A discrete-time illustration of this assumption expresses observed price data

Turnover is the ratio of the amount traded (or volume) to the average amount traded during a given time period [

The identity of the Lagrange multiplier

These last two sentences paraphrase and adapt the original observations of Reginatto regarding the ontological and epistemological content of quantum theory [