This paper presents a tractable model of non-linear dynamics of market returns using a Langevin approach.Due to non-linearity of an interaction potential, the model admits regimes of both small and large return fluctuations. Langevin dynamics are mapped onto an equivalent quantum mechanical (QM)...

Classical quantitative finance models such as the Geometric Brownian Motion or its later extensions such as local or stochastic volatility models do not make sense when seen from a physics-based perspective, as they are all equivalent to a negative mass oscillator with a noise. This paper...

This is a supplementary note for the paper "QLBS: Q-Learner in the Black-Scholes(-Merton) Worlds" found here:'http://ssrn.com/abstract=3087076' http://ssrn.com/abstract=3087076,that explains how a model developed there applies to the problem of relative pricing of options in a data-driven...