Simplified stock markets described by number operators

TL;DR

This paper extends an operatorial approach to a simplified stock market model, analyzing trader portfolios and observables using fixed point approximations, with the stock prices treated as inputs.

Contribution

It introduces a mixed toy model of a stock market with fixed share prices and applies an operatorial method to analyze its dynamics.

Findings

Derived the time evolution of trader portfolios

Solved equations of motion using fixed point approximation

Provided insights into simplified stock market dynamics

Abstract

In this paper we continue our systematic analysis of the operatorial approach previously proposed in an economical context and we discuss a {\em mixed} toy model of a simplified stock market, i.e. a model in which the price of the shares is given as an input. We deduce the time evolution of the portfolio of the various traders of the market, as well as of other {\em observable} quantities. As in a previous paper, we solve the equations of motion by means of a {\em fixed point like} approximation.