The minimal length uncertainty and the quantum model for the stock market

TL;DR

This paper extends a quantum stock market model to incorporate the discrete nature of stock prices, revealing how minimal trading units influence system frequencies and their relation to information dynamics.

Contribution

It introduces a generalized quantum model for stock prices that accounts for minimal trading units and explores their effects on system frequencies and information transition probabilities.

Findings

Minimal trading value causes positive frequency shifts

Generalized uncertainty relation applies to stock prices

Connection established between information frequency and transition probabilities

Abstract

We generalize the recently proposed quantum model for the stock market by Zhang and Huang to make it consistent with the discrete nature of the stock price. In this formalism, the price of the stock and its trend satisfy the generalized uncertainty relation and the corresponding generalized Hamiltonian contains an additional term proportional to the fourth power of the trend. We study a driven infinite quantum well where information as the external field periodically fluctuates and show that the presence of the minimal trading value of stocks results in a positive shift in the characteristic frequencies of the quantum system. The connection between the information frequency and the transition probabilities is discussed finally.