Finite quantum mechanical model for the stock market

TL;DR

This paper introduces a finite quantum mechanical model for stock markets, using quantum formalism to describe the relationship between stock price and ownership, and numerically solves the Schrödinger-type equation for stock price evolution.

Contribution

It applies finite-dimensional quantum mechanics to model stock market dynamics, capturing partial information and the price-ownership relationship in a novel way.

Findings

Model captures the uncertainty in stock ownership and price.

Numerical solutions demonstrate the evolution of stock prices over time.

Quantum formalism provides new insights into market behavior.

Abstract

The price of a given stock is exactly known only at the time of sale when the stock is between the traders. If we know the price (owner) then we have no information on the owner (price). A more general description including cases when we have partial information on both price and ownership is obtained by using the quantum mechanics methods. The relation price-ownership is similar to the relation position-momentum. Our approach is based on the mathematical formalism used in the case of quantum systems with finite-dimensional Hilbert space. The linear operator corresponding to the ownership is obtained from the linear operator corresponding to the price by using the finite Fourier transform. In our idealized model, the Schrodinger type equation describing the time evolution of the stock price is solved numerically.