Portfolio Optimization with Multi-Trend Objective and Accelerated Quasi-Newton Method

• Published in: Symmetry (Basel) Vol. 16; no. 7; p. 821
• Main Authors: Lin, Caiming, He, Xinyi
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.07.2024
• Subjects: accelerated quasi-Newton method; Algorithms; Artificial intelligence; Asymmetry; Convergence (Social sciences); Exploitation; Financial markets; Forecasts and trends; Growth factors; Investment analysis; Machine learning; Methods; multi-trend objective price prediction; Optimization; Optimization techniques; Parameter estimation; Passive-aggressive behavior; Performance evaluation; portfolio optimization; Portfolio performance; Prices; Quasi Newton methods; Regularization; Securities markets; State-of-the-art reviews; Trends; Wolfe conditions
• ISSN: 2073-8994; 2073-8994
• DOI: 10.3390/sym16070821

We propose a portfolio optimization method with a multi-trend objective and an accelerated quasi-Newton method (MTO-AQNM). It leverages a BFGS-based quasi-Newton algorithm and incorporates an ℓ1 regularization term and the self-funding constraint. The MTO is designed to identify multiple trend reversals. Different trend reversals are asymmetric, and we hoped to extract rich and effective information from them. The AQNM adopts the BFGS method with the Wolfe conditions, which reduces computational complexity and improves convergence speed. We wanted to evaluate the performance of our algorithm through financial markets that were asymmetric in all respects. To this end, we conducted comprehensive experimental approaches on six benchmark data sets of real-world financial markets that were asymmetric in time, frequency, and asset type. Our method demonstrated superior performance over other state-of-the-art competitors across several mainstream evaluation metrics.