Stock markets and quantum dynamics: a second quantized description

TL;DR

This paper models stock markets using quantum operator techniques, extending previous work to more realistic multi-trader scenarios and deriving approximate solutions for portfolio dynamics.

Contribution

It introduces a quantum-inspired model for stock markets with multiple traders and provides approximate solutions for portfolio evolution using stochastic limit and fixed point methods.

Findings

Derived approximate solutions for trader portfolios

Extended quantum market models to multiple traders

Applied stochastic limit and fixed point approximations

Abstract

In this paper we continue our descriptions of stock markets in terms of some non abelian operators which are used to describe the portfolio of the various traders and other {\em observable} quantities. After a first prototype model with only two traders, we discuss a more realistic model of market with an arbitrary number of traders. For both models we find approximated solutions for the time evolution of the portfolio of each trader. In particular, for the more realistic model, we use the {\em stochastic limit} approach and a {\em fixed point like} approximation.