Hybrid ridgelet deep neural networks for data-driven arbitrage strategies

Abstract In this study, we propose an alternative solution to the model framework discussed in Neufeld et al. (Neufeld et al. 2024 SIAM J. Financ. Math.15, 436–472. (doi:10.1137/22M1487928)) by integrating deep neural networks with the ridgelet transform. The ridgelet transform is used for statistical arbitrage detection on high-dimensional, sparse structures, utilizing Borel-measurable functions. This transform also enhances the expressive power of neural networks, enabling them to capture complex and high-dimensional market structures. Theoretically, we determine profitable trading strategies by optimizing hybrid ridgelet deep neural networks. Further, we emphasize the role of ridgelet activation functions in ensuring stability and adaptability under uncertainty. We utilize a high-performance computing cluster for detecting arbitrage across multiple assets, ensuring scalability and efficient processing of large-scale financial data. The proposed method is also suitable for retail investors with smaller portfolios and limited computational resources. Empirical results demonstrate strong profitability across diverse scenarios involving up to 50 assets, with particularly robust performance during periods of market volatility.