An operatorial approach to stock markets

TL;DR

This paper introduces toy models of stock markets using an operatorial approach inspired by quantum mechanics, focusing on discrete quantities and conserved properties like total shares and cash.

Contribution

It applies quantum-inspired operatorial methods to model stock market dynamics, emphasizing discrete exchange and conservation laws.

Findings

Models capture discrete share and cash exchanges.

Framework parallels quantum gas models.

Potential for analyzing market conservation laws.

Abstract

We propose and discuss some toy models of stock markets using the same operatorial approach adopted in quantum mechanics. Our models are suggested by the discrete nature of the number of shares and of the cash which are exchanged in a real market, and by the existence of conserved quantities, like the total number of shares or some linear combination of cash and shares. The same framework as the one used in the description of a gas of interacting bosons is adopted.