  Financial markets have long since been modeled using stochastic methods such
as Brownian motion, and more recently, rough volatility models have been built
using fractional Brownian motion. This fractional aspect brings memory into the
system. In this project, we describe and analyze a financial model based on the
fractional Langevin equation with colored noise generated by fractional
Brownian motion. Physics-based methods of analysis are used to examine the
phase behavior and dispersion relations of the system upon varying input
parameters. A type of anomalous marginal glass phase is potentially seen in
some regions, which motivates further exploration of this model and expanded
use of phase behavior and dispersion relation methods to analyze financial
models.
