Classical and quantum randomness and the financial market

TL;DR

This paper explores whether quantum-like probabilistic models better describe financial market complexity than classical models, proposing a new statistical test to empirically evaluate the 'quantumness' of financial data.

Contribution

It introduces a quantum-like probabilistic framework for financial markets and develops a Bell inequality-based statistical test to assess its applicability.

Findings

Quantum-like models may better capture financial market behavior.

A new Bell inequality-based test for financial data is proposed.

The hypothesis of 'quantumness' in financial data requires experimental validation.

Abstract

We analyze complexity of financial (and general economic) processes by comparing classical and quantum-like models for randomness. Our analysis implies that it might be that a quantum-like probabilistic description is more natural for financial market than the classical one. A part of our analysis is devoted to study the possibility of application of the quantum probabilistic model to agents of financial market. We show that, although the direct quantum (physical) reduction (based on using the scales of quantum mechanics) is meaningless, one may apply so called quantum-like models. In our approach quantum-like probabilistic behaviour is a consequence of contextualy of statistical data in finances (and economics in general). However, our hypothesis on "quantumness" of financial data should be tested experimentally (as opposed to the conventional description based on the noncontextual classical probabilistic approach). We present a new statistical test based on a generalization of the well known in quantum physics Bell's inequality.