A quantum mechanical model for the relationship between stock price and stock ownership

TL;DR

This paper proposes a quantum mechanical model for stock prices, representing the relationship between stock ownership and price as a probability function evolving according to a Schrödinger-like equation.

Contribution

It introduces a novel quantum-inspired framework to model stock prices and ownership, extending traditional financial models with quantum mechanics principles.

Findings

Stock price can be modeled as a probability function.

The evolution of stock prices follows a Schrödinger-type equation.

Partial information on ownership affects price predictions.

Abstract

The trade of a fixed stock can be regarded as the basic process that measures its momentary price. The stock price is exactly known only at the time of sale when the stock is between traders, that is, only in the case when the owner is unknown. We show that the stock price can be better described by a function indicating at any moment of time the probabilities for the possible values of price if a transaction takes place. This more general description contains partial information on the stock price, but it also contains partial information on the stock owner. By following the analogy with quantum mechanics, we assume that the time evolution of the function describing the stock price can be described by a Schrodinger type equation.