Research-topics

Deep learning has emerged as a powerful tool for analyzing high-frequency financial data, offering sophisticated capabilities to capture complex patterns and nonlinear relationships in market dynamics. These advanced models, particularly those based on Transformer networks, recurrent neural networks (RNNs), and long short-term memory (LSTM) networks, can process massive amounts of time-series data to predict market movements, assess volatility, and automate trading decisions with remarkable precision.

Portfolio optimization stands as a cornerstone of modern investment management, focusing on the systematic selection of optimal asset allocations that balance expected returns against financial risk. Since Harry Markowitz’s groundbreaking 1952 paper on Portfolio Selection, for which he later received the Nobel Prize in Economic Sciences, the field has evolved significantly beyond the traditional mean-variance framework.

Financial markets are inherently interconnected systems where assets, institutions, and market participants form complex networks of relationships that evolve over time. Graph learning has emerged as a powerful framework for understanding and modeling these financial networks, enabling the discovery of meaningful relationships among stocks, cryptocurrencies, or other financial instruments through their return time series, trading volumes, or other market indicators.

Signal processing and financial engineering are seemingly different areas that share strong connections underneath. Both areas rely on the statistical analysis and modeling of systems and signals, either from the financial markets or from communication channels.

Traditional convex optimization methods and signal processing techniques can be employed in big data problems characterized by large amounts of data in high-dimensional spaces. However, big data brings additional difficulties that need to be taken care of such as high-computational cost that require simple and efficient methods, distributed implementations, faulty data in the form of outliers, etc.

The design of communication systems depends strongly on the degree of knowledge of the channel state information (CSI). The best spectral efficiency and/or performance is obviously achieved when perfect CSI is available at both sides of the link.

Carefully designed sequences lie at the heart of virtually any digital system commonly used in our daily lives. Examples include GPS synchronization, multiuser CDMA systems, radar ambiguity function shaping, cryptography for secure transactions, and even the watermarking of digital images or videos.

Multiple-input multiple-output (MIMO) channels provide an abstract and unified representation of different physical communication systems, ranging from multi-antenna wireless channels to wireless digital subscriber line systems. They have the key property that several data streams can be simultaneously established.

Semidefinite programming (SDP) is a class of convex optimization problems with a rich theory that can be efficiently solved in polynomial time. Many problems in wireless communications and radar systems can be formulated as SDPs with additional rank constraints.

The Variation Inequality (VI) problem constitutes a very general class of problems in nonlinear analysis. The VI framework embraces many different types of problems such as systems of equations, optimization problems, equilibrium programming, complementary problems, saddle-point problems, Nash equilibrium problems, and generalized Nash equilibrium problems.