Modelling Illiquid Stocks Using Quantum Stochastic Calculus: Asymptotic Methods

Paper: arXiv 2302.05256

Authors: Will Hicks

Abstract

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. Whilst the series in question are in general divergent, we show they can be used to approximate solutions for longer time frames, and provide estimates for the relative error on the higher order terms.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper demonstrates high mathematical sophistication by applying quantum stochastic calculus, non-zero conservation processes, and asymptotic power series solutions to market illiquidity. However, it lacks empirical validation, backtesting, or historical market data to support its theoretical findings.

Research Flowchart

  flowchart TD
    A[Goal: Model Illiquid Financial Markets<br/>via Quantum Stochastic Calculus] --> B[Input: Fokker-Planck Equations<br/>with Non-Zero Conservation Process]
    B --> C[Method: Apply Asymptotic Methods<br/>& Power Series Expansions]
    C --> D[Compute: Higher-Order Term Analysis<br/>& Relative Error Estimates]
    D --> E[Outcome: Approximate Long-Term Solutions<br/>from Divergent Series]