A quantum statistical approach to simplified stock markets

TL;DR

This paper applies quantum statistical methods, including perturbation techniques and Feynman graphs, to analyze a simplified stock market model based on bosonic operators, focusing on portfolio transition probabilities.

Contribution

It introduces a novel quantum statistical framework for modeling stock markets, utilizing perturbation theory and graphical methods to analyze portfolio dynamics.

Findings

Transition probabilities between portfolios are computed using quantum techniques.

Feynman graph methods are adapted for financial modeling.

The approach offers a new perspective on stock market dynamics.

Abstract

We use standard perturbation techniques originally formulated in quantum (statistical) mechanics in the analysis of a toy model of a stock market which is given in terms of bosonic operators. In particular we discuss the probability of transition from a given value of the {\em portfolio} of a certain trader to a different one. This computation can also be carried out using some kind of {\em Feynman graphs} adapted to the present context.