Modelling Illiquid Stocks Using Quantum Stochastic Calculus: Asymptotic Methods

TL;DR

This paper applies quantum stochastic calculus to model illiquid stocks, deriving asymptotic solutions to Fokker-Planck equations and providing methods to approximate these solutions over extended periods.

Contribution

It introduces a power series approach for quantum stochastic processes with conservation, including error estimates for practical approximation.

Findings

Power series solutions can approximate quantum stochastic processes.

Series divergence does not hinder long-term approximation.

Error estimates improve solution reliability for extended time frames.

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.