Deep Learning in Hilbert Spaces

This book delves into the fusion of advanced mathematical concepts and cutting-edge deep learning techniques to transform algorithmic trading. By extending deep learning models into Hilbert spaces-complete infinite-dimensional spaces endowed with inner products-the book presents a novel framework for handling the complex, high-dimensional data inherent in financial markets. This approach opens new avenues for modeling and predicting market behaviors with greater accuracy and computational efficiency.



Main Topics:

Foundations of Hilbert Spaces in Financial Modeling: This section introduces the core principles of Hilbert spaces and their applicability to finance, explaining how infinite-dimensional spaces can model complex financial phenomena more effectively than traditional finite-dimensional methods.

Extending Deep Learning Architectures to Hilbert Spaces: Exploring how standard deep learning models like neural networks can be generalized to operate within Hilbert spaces, enabling the processing of functional data and continuous-time signals crucial for high-frequency trading.

Kernel Methods and Reproducing Kernel Hilbert Spaces (RKHS): Discussing the role of RKHS in enhancing machine learning models, particularly in capturing nonlinear relationships in financial data through kernel functions that map inputs into higher-dimensional Hilbert spaces.