Quantum Majorization in Market Crash Prediction

Abstract

We introduce the Quantum Alarm System, a novel framework that combines the informational advantages of quantum majorization applied to tail pseudo-correlation matrices with the learning capabilities of a reinforced urn process, to predict financial turmoil and market crashes. This integration allows for a more nuanced analysis of the dependence structure in financial markets, particularly focusing on extreme events reflected in the tails of the distribution. Our model is tested using the daily log-returns of the 30 constituents of the Dow Jones Industrial Average, spanning from 2 January 1992 to 30 August 2024. The results are encouraging: in the validation set, the 12-month ahead probability of correct alarm is between (Formula presented.) and (Formula presented.), while maintaining a low false alarm rate. Thanks to the application of quantum majorization, the alarm system effectively captures non-traditional and emerging risk sources, such as the financial impact of the COVID-19 pandemic—an area where traditional models often fall short.