Information Entropy of the Financial Market: Modelling Random Processes Using Open Quantum Systems

TL;DR

This paper explores how open quantum systems can model the information entropy and dynamics of financial markets, offering a flexible alternative to classical models and revealing non-classical behaviors through simulations.

Contribution

It introduces a novel quantum framework for modeling financial market entropy and demonstrates its ability to produce non-classical results beyond traditional methods.

Findings

Quantum models can simulate classical diffusion in markets.

Relaxing assumptions yields non-classical entropy behaviors.

Numerical simulations highlight new market dynamics.

Abstract

We discuss the role of information entropy on the behaviour of random processes, and how this might take effect in the dynamics of financial market prices. We then go on to show how the Open Quantum Systems approach can be used as a more flexible alternative to classical methods in terms of modelling the entropy gain of a random process. We start by describing an open quantum system that can be used to model the state of a financial market. We then go on to show how to represent an essentially classical diffusion in this framework. Finally, we show how by relaxing certain assumptions, one can generate interesting and essentially non-classical results, which are highlighted through numerical simulations.