Portfolio Optimization under Polynomial Trading Costs with Mean-Reverting Assets

Abstract

This thesis explores optimal portfolio allocation under polynomial trading costs created by market illiquidity, focusing on mean-reverting assets modeled by an Ornstein-Uhlenbeck process. Traditional portfolio optimization models often assume proportional transaction costs or ignore them entirely, leading to strategies that may be impractical due to excessive trading. We extend previous research by incorporating higher-order polynomial cost functions to better reflect the impact of trading volume on costs. Using deep neural networks, we approximate optimal no-trade boundaries and compare performance against cost-free analytic solutions. Our findings suggest that incorporating polynomial trading costs significantly alters optimal rebalancing behavior, particularly at higher wealth levels, where the importance of asset diversification increases. Backtesting results demonstrate that learned strategies outperform traditional cost-free models and trained linear models by reducing excessive trading and improving long-term wealth accumulation. This research provides insights into the scalability of deep learning approaches for real-world portfolio optimization problems and informs on ways to address market limitations.