  With the recent rise of Machine Learning as a candidate to partially replace
classic Financial Mathematics methodologies, we investigate the performances of
both in solving the problem of dynamic portfolio optimization in
continuous-time, finite-horizon setting for a portfolio of two assets that are
intertwined.
  In Financial Mathematics approach we model the asset prices not via the
common approaches used in pairs trading such as a high correlation or
cointegration, but with the cointelation model that aims to reconcile both
short-term risk and long-term equilibrium. We maximize the overall P&L with
Financial Mathematics approach that dynamically switches between a
mean-variance optimal strategy and a power utility maximizing strategy. We use
a stochastic control formulation of the problem of power utility maximization
and solve numerically the resulting HJB equation with the Deep Galerkin method.
  We turn to Machine Learning for the same P&L maximization problem and use
clustering analysis to devise bands, combined with in-band optimization.
Although this approach is model agnostic, results obtained with data simulated
from the same cointelation model as FM give an edge to ML.
