A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Researchers study the normalizing constant of a continuous categorical distribution.
Based on criteria of mathematical simplicity and consistency with empirical market data, a model with volatility driven by fractional noise has been constructed which provides a fairly accurate mathematical parametrization of the data. Here, some features of the model are discussed and, using agent-based models, one tr…
A new machine learning model uses matrix exponentials for universal approximation.
Based on criteria of mathematical simplicity and consistency with empirical market data, a stochastic volatility model is constructed, the volatility process being driven by fractional noise. Price return statistics and asymptotic behavior are derived from the model and compared with data. Deviations from Black-Scholes…
Based on a criterion of mathematical simplicity and consistency with empirical market data, a stochastic volatility model has been obtained with the volatility process driven by fractional noise. Depending on whether the stochasticity generators of log-price and volatility are independent or are the same, two versions …
Based on a criterium of mathematical simplicity and consistency with empirical market data, a stochastic volatility model has been obtained with the volatility process driven by fractional noise. Depending on whether the stochasticity generators of log-price and volatility are independent or are the same, two versions …
We develop theory and applications of forward characteristic processes in discrete time following a seminal paper of Jan Kallsen and Paul Krühner. Particular emphasis is placed on the dynamics of volatility surfaces which can be easily formulated and implemented from the chosen discrete point of view. In mathematical t…
The paper develops formulas for hyperbolic simplices based on edge lengths.
Paper finds sample complexity for learning high-dimensional simplices from noisy data.
Estimates dimensions of maximal simplices for rational and irrational trees in Outer space.
The paper establishes conditions for Riemannian connections and semi-simplicity of Lie algebras using spray structures.
It is proved that the volume of spherical or hyperbolic simplices, when considered as a function of the dihedral angles, can be extended continuously to degenerated simplices.
A simple method makes Euclidean patterns look like Escher's art.
Principal circle bundle over a PL polyhedron can be triangulated and thus obtains combinatorics. The triangulation is assembled from triangulated circle bundles over simplices. To every triangulated circle bundle over a simplex we associate a necklace (in combinatorial sense). We express rational local formulas for all…
Geodesic simplices in pseudo-hyperbolic space get a cohomological treatment.
SmartDCA improves investment returns by adjusting purchases based on prices.
Replacing Black-Scholes' driving process, Brownian motion, with fractional Brownian motion allows for incorporation of a past dependency of stock prices but faces a few major downfalls, including the occurrence of arbitrage when implemented in the financial market. We present the development, testing, and implementatio…
Study PL bordism theories with quantitative bounds on filling simplices.
Framework reduces simplicity bias in NNs, improving OOD generalization and robustness.
New framework shows -simplicity for groups without certain subalgebras.
In this article, we prove a theorem comparing the dihedral angles of simplices in the hyperbolic, spherical and Euclidean geometries.
Pricing financial or real options with arbitrary payoffs in regime-switching models is an important problem in finance. Mathematically, it is to solve, under certain standard assumptions, a general form of optimal stopping problems in regime-switching models. In this article, we reduce an optimal stopping problem with …
We study a natural intrinsic definition of geometric simplices in Riemannian manifolds of arbitrary dimension , and exploit these simplices to obtain criteria for triangulating compact Riemannian manifolds. These geometric simplices are defined using Karcher means. Given a finite set of vertices in a convex set on t…
AB-testing is a very popular technique in web companies since it makes it possible to accurately predict the impact of a modification with the simplicity of a random split across users. One of the critical aspects of an AB-test is its duration and it is important to reliably compute confidence intervals associated with…
Research reveals simplicity bias in random logistic map, impacting data analysis and forecasting.
The Apollonius theorem is generalized for m-simplices, with applications in geometry and optimization.
Similar simplices can be inscribed in most smoothly embedded spheres.
This anniversary paper is an occasion to recall some of the events that shaped institutional econophysics. But in these thoughts about the evolution of econophysics in the last 15 years we also express some concerns. Our main worry concerns the relinquishment of the simplicity requirement. Ever since the groundbreaking…
We study prismatics sets analogously to simplical sets except that realization involves prisms, i.e., products of simplices rather than just simplices. Particular examples are the prismatic subdivision of a simplicial set S and the prismatic star of S. Both have the same homotopy type as S and in particular the latter …
A new model explains protein interactions via electron delocalization.
Simplicial sets deformation retract onto transverse simplices.
We generalize the very well known boundary operator of the ordinary singular homology theory, defined in many books about algebraic topology. We describe a variant of this ordinary simplicial boundary operator where the usual boundary (n-1)-simplices of each n-simplex are replaced by combinations of internal (n-1)- sim…
The paper explores how simplicity leads to better out-of-distribution generalization in models.
The study reveals simplicity bias in neural networks leading to better compositional mappings.
Study on simplicity of Lie skew braces, proving new results for compact cases.
Triangulations of R^n have at least tensor rank of determinant simplices.
Two-layer networks favor simple features, especially in complex datasets.
Adam avoids simplicity bias in neural networks, leading to better generalization.
We give several new criteria to judge whether a simple convex polytope in a Euclidean space is combinatorially equivalent to a product of simplices. These criteria are mixtures of combinatorial, geometrical and topological conditions that are inspired by the ideas from toric topology.
Neural nets learn simple distributions first, then more complex ones.
The paper proves eigenvalues are simple for specific operators on bundles.
Unified framework for removing unwanted information from machine learning models.
Ancient formula connects volume forms and infinitesimal square volumes in manifolds.
K-means algorithm improves financial market risk prediction accuracy.
Everyone knows that the Euler characteristic of a combinatorial manifold is given by the alternating sum of its numbers of simplices. It is shown that there are other linear combinations of the numbers of simplices which are combinatorial invariants, but that all such invariants are multiples of the Euler characteristi…
This paper presents an extension and an elaboration of the theory of differential similarity, which was originally proposed in arXiv:1401.2411 [cs.LG]. The goal is to develop an algorithm for clustering and coding that combines a geometric model with a probabilistic model in a principled way. For simplicity, the geomet…
Maps discrete manifolds to partitions to define new manifolds.
Compressed imitation learning uses simplicity priors for efficient expert behavior copying.