Black Scholes formula and Variational Principle

Physics of Finance, Gauge Modelling in Non-equilibrium Pricing by Kirill Ilinski (quoting) Further, we are going to demonstrate how the tools of modern theoretical physics, its images and objects, physical "blocks" are used to build a theory describing the short-term ("fast") dynamics of money flows and addressing three questions "Why?" of financial physics. Adjustments to the Black-Scholes equation will appear naturally when we reformulate financial derivative pricing policy in terms of a new theory. (end quote) Also:

John Bailey