Financial Mathematics (Click on Pictures)

Scientific Machine Learning for Continuous Universal Portfolios: In this paper, we illustrate how combining scientific machine learning with Dynamic Mode Decomposition solves high-dimensional portfolio optimization under real-world frictions. We model asset prices using a dual-noise framework to account for both instantaneous volatility and persistent trend-following dynamics. Our algorithm establishes an optimal No-Trade Region, allowing portfolio weights to float naturally until fundamental regime changes require execution. Consequently, our model scales polynomially to handle portfolios with over a hundred assets in real time, drastically reducing trading fees while preserving alpha during market stress. With J.-G. Aguilar and M. Gunzburger Communications on Applied Mathematics and Computation, Accepted, 2026.