2019/05/17 by Will Hicks, Hicks, Will
Economics, Econometrics and Finance · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Economics and business #Mathematical Finance (q-fin.MF) #Quantum Mechanics and Applications #Statistical Mechanics and Entropy #q-fin.MF
paper · pdf · doi:10.48550/arxiv.1905.07257
19 pages
arxiv created 2019/05/17 · openalex publication_date 2019/05/17 · arxiv updated 2019/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Accardi-Boukas quantum Black-Scholes equation can be used as an alternative to the classical approach to finance, and has been found to have a number of useful benefits. The quantum Kolmogorov backward equations, and associated quantum Fokker-Planck equations, that arise from this general framework, are derived using the Hudson-Parthasarathy quantum stochastic calculus. In this paper we show how these equations can be derived using a nonlocal approach to quantum mechanics. We show how nonlocal diffusions, and quantum stochastic processes can be linked, and discuss how moment matching can be used for deriving solutions.