Dynamic mode decomposition for online portfolio selection task

Online portfolio selection (OPS) is a complex task aimed at maximizing investment returns through strategic allocation of capital among risky assets. Traditional Follow the Winner (FTW) strategies, grounded in the Best Constant Rebalanced Portfolios strategy, assume market is independent and identically distributed (i.i.d.), which often fails to capture real-world financial market dynamics, leading to sub-optimal performance in practical applications. To address this limitation, we propose integrating Dynamic Mode Decomposition (DMD) into FTW strategies. DMD is a powerful data-driven technique that originated in the field of fluid dynamics. It is designed to extract coherent structures and identify temporal patterns within complex data. By applying DMD to financial market data, we can uncover underlying patterns and trends that are not apparent under the i.i.d. assumption. Significantly, the integrated DMD in this paper allows for efficient recursion, which is particularly crucial for OPS task. To illustrate the effectiveness of the proposed idea, we consider the Exponential Gradient (EG) strategy as an example and proposed Exponential Gradient with Dynamic Mode Decomposition (EGDMD). The results demonstrate that the proposed EGDMD outperforms traditional EG-type strategies, significantly improves risk-adjusted returns, and maintains computational efficiency. The integration of DMD allows for more accurate identification of market patterns, leading to more effective investment decisions and enhanced portfolio performance.