Papers, ranked by score

Ordered by a blend of empirical rigor (60%) and math complexity (40%).

Modelling Uncertain Volatility Using Quantum Stochastic Calculus: Unitary vs Non-Unitary Time Evolution

In this article we look at stochastic processes with uncertain parameters, and consider different ways in which information is obtained when carrying out observations. For example we focus on the case of a the random evolution of a traded financial asset price with uncertain volatility. The quantum

Lab Rats Math 8.5 Rigor 3 ·  July 5, 2024

Modelling Illiquid Stocks Using Quantum Stochastic Calculus

Quantum Stochastic Calculus can be used as a means by which randomness can be introduced to observables acting on a Hilbert space. In this article we show how the mechanisms of Quantum Stochastic Calculus can be used to extend the classical Black-Scholes framework by incorporating a breakdown in the

Lab Rats Math 8.5 Rigor 2.5 ·  February 10, 2023

Modelling Financial Market Imperfection Using Open Quantum Systems

We start with the idea that open quantum systems can be used to represent financial markets by modelling events from the external environment and their impact on the market price. We show how to characterize distinct orbits of the time evolution, and look at the development of the reduced density ma

Lab Rats Math 8.5 Rigor 2 ·  May 2, 2025

Modelling Illiquid Stocks Using Quantum Stochastic Calculus: Asymptotic Methods

This article investigates the Fokker-Planck equations that arise from the application of quantum stochastic calculus to the modelling of illiquid financial markets, using asymptotic methods. We present a power series solution for quantum stochastic processes with a non-zero conservation process. Whi

Lab Rats Math 8.5 Rigor 2 ·  February 10, 2023

Information Entropy of the Financial Market: Modelling Random Processes Using Open Quantum Systems

We discuss the role of information entropy on the behaviour of random processes, and how this might take effect in the dynamics of financial market prices. We then go on to show how the Open Quantum Systems approach can be used as a more flexible alternative to classical methods in terms of modellin

Lab Rats Math 7.5 Rigor 1.5 ·  June 28, 2024

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