# Portfolio Optimization for Cointelated Pairs: SDEs vs. Machine Learning

## TL;DR

This paper compares traditional Financial Mathematics and Machine Learning methods for dynamic portfolio optimization of two intertwined assets, highlighting the strengths of ML when data is simulated from a cointelation model.

## Contribution

It introduces a novel comparison between SDE-based Financial Mathematics and Machine Learning approaches for cointelated pairs portfolio optimization.

## Key findings

- ML approach outperforms FM with data from the cointelation model
- Financial Mathematics uses a stochastic control and Deep Galerkin method
- Clustering and in-band optimization are key ML techniques used

## Abstract

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.