Blog Posts

Tensor theory, originating in mathematics and physics, finds its application in finance through its ability to represent and analyze complex, multi-dimensional data. A tensor is a generalization of scalars (zero-order tensors), vectors (first-order tensors), and matrices (second-order tensors) to higher dimensions.   Key Takeaways – Tensor Theory in Finance, Markets & Trading Multidimensional Data Analysis […]

Riemannian manifolds are mathematical constructs from the field of differential geometry, which have applications in various disciplines, including finance and quant trading. We’ll cover both the fundamental concepts of Riemannian manifolds and their practical applications in financial contexts.   Key Takeaways – Riemannian Manifolds in Finance, Markets & Trading Geometric Framework Riemannian manifolds provide a […]

Geometric mechanics is a branch of mathematics, most typically applied to theoretical physics, that applies geometric methods to problems in mechanics and dynamics. It combines differential geometry, the study of smooth manifolds, with the principles of classical and quantum mechanics. The key concepts and applications of geometric mechanics in finance offer a different perspective on […]

Statistical Mechanics, also known as Statistical Physics, looks into the microscopic details of systems to predict macroscopic behaviors. Beyond traditional physics, Statistical Mechanics finds applications in finance, modeling complex systems from particles to assets and broader physical systems to portfolios.   Key Takeaways – Statistical Mechanics & Applications to Finance Statistical mechanics can provide new […]

Manifold learning is a branch of machine learning that involves the analysis and understanding of high-dimensional data by finding low-dimensional representations without losing meaningful properties.   Key Takeaways – Manifold Learning in Finance, Markets & Trading Dimensionality Reduction Manifold learning can simplify complex financial datasets. Reveal underlying structures and relationships critical for informed trading decisions. […]

Symplectic geometry, originating in classical mechanics, is a branch of differential geometry concerned with symplectic manifolds (a way of representing and visualizing non-linear data). A symplectic manifold is a smooth manifold equipped with a closed, non-degenerate 2-form, known as a symplectic form. This field has found applications in various areas, including finance, particularly in the […]

Differential topology is a field of mathematics concerned with the study of differentiable functions and differentiable manifolds. It has several key concepts that can be theoretically and practically applied to finance and markets, mostly in the form of advanced visual data interpretation.   Key Takeaways – Differential Topology in Finance, Markets & Trading Model Flexibility […]

“Probabilities of probabilities,” often referred to as uncertainty of uncertain events or stochastic uncertainty, is a fascinating concept in finance and markets. Trading and investing is fundamentally an exercise of applied probability, and we have probability distributions to represent this process. However, the probabilities themselves are often unknown. It recognizes the multi-dimensional and nested layers […]

Information geometry applies the concepts and methods of differential geometry to problems in probability theory and statistics, which are important in finance. It explores the geometric structure of statistical models and studies how these structures influence inference and decision-making processes. The key concept in information geometry is the notion of a statistical manifold, which is […]

Currency risk premium refers to the additional return a trader or investor demands for holding a currency that may depreciate against their home currency. This concept is important in international finance and investing. The risk premium is influenced by various factors:   Key Takeaways – Currency Risk Premia Currency risk premia reflect the potential return […]