Portfolio Optimization with Mean-reverting Assets: Combining Theory with Deep Learning.

Abstract

We study the finite-horizon dynamic portfolio model involving mean reverting

(Ornstein-Uhlenbeck) assets in the presence of transaction costs. The goal is to

maximize the expected constant relative risk aversion (CRRA) utility of terminal

wealth. We investigate the problem in two parts. In the first part, we analyze the

problem without transaction costs for three types of portflios: we analytically solve

the problem for a single risky asset and a risk free asset, and then derive the solution

to a portfolio of OU assets and a portfolio of OU and geometric Brownian motion

(GBM) assets via a system of ordinary differential equations (ODEs). In the second

part, we extend the problem by adding proportioanl transaction cost. The portfolio

optimization problem becomes intractable both analytically and computationally

when there exist transaction costs and multiple assets. To address transaction costs,

we propose a novel numerical approach employing deep neural networks, building on

the previous ODE solution and given the standard no-trade zone policy rules. Our

method readily extends to high-dimensional portfolio problems wherein traditional

methods fail. Experiments with synthetic and market data show the numerical

benefits of the developed algorithms.