Title: Portfolio Optimization for Cointelated Pairs: SDEs vs. Machine Learning,
Abstract: We investigate the problem of dynamic portfolio optimization in
continuous-time, finite-horizon setting for a portfolio of two stocks and one
risk-free asset. The stocks follow the Cointelation model. The proposed
optimization methods are twofold. In what we call an Stochastic Differential
Equation approach, we compute the optimal weights using mean-variance criterion
and power utility maximization. We show that dynamically switching between
these two optimal strategies by introducing a triggering function can further
improve the portfolio returns. We contrast this with the machine learning
clustering methodology inspired by the band-wise Gaussian mixture model. The
first benefit of the machine learning over the Stochastic Differential Equation
approach is that we were able to achieve the same results though a simpler
channel. The second advantage is a flexibility to regime change.