Pseudo-Hermiticity, Martingale Processes and Non-Arbitrage Pricing

TL;DR

This paper explores a quantum probability framework for financial modeling, enabling the construction of martingales without Brownian integrals, and discusses potential benefits and future research directions.

Contribution

It introduces a novel approach using quantum probability to build martingales in finance, bypassing traditional Brownian motion reliance.

Findings

Quantum probability can construct martingales without Brownian integrals

The approach offers new insights into non-arbitrage pricing

Potential for improved financial modeling techniques

Abstract

Financial models based on the Wick product, and White Noise formalism have previously been suggested in order to incorporate integrals with respect to fractional Brownian motion. It has also been pointed out that this leads naturally to a quantum mechanical interpretation of the financial market. In this article we pursue this idea further, and in particular show how the framework of quantum probability can be used to construct Martingales, without relying on Brownian integrals. We go on to suggest benefits of doing so, and avenues for future work.