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.
Study of discrete period matrices on embedded graphs, relating to Riemann surfaces.
The paper calculates period matrices for specific algebraic curves.
We calculate eigenvector overlaps between intersecting time periods of covariance matrices.
We construct and study a family of double-periodic almost entire solutions of the maximal surface equation. The solutions are parameterized by a submanifold of -matrices (the so-called generating matrices). We show that the constructed solutions are either space-like or of mixed type with the light-cone type…
Algorithm constructs and classifies weaving diagrams using combinatorial methods.
In the previous work, the first author established an algorithm to compute the Morse index and the nullity of an -periodic minimal surface in . In fact, the Morse index can be translated into the number of negative eigenvalues of a real symmetric matrix and the nullity can be translated into the number…
We study the one parameter family of genus 2 Riemann surfaces defined by the orbit of the L-shaped translation surface tiled by three squares under the Teichmüller geodesic flow. These surfaces are real algebraic curves with three real components. We are interested in describing these surfaces by their period matrices.…
We recall the theory of linear discrete Riemann surfaces and show how to use it in order to interpret a surface embedded in R^3 as a discrete Riemann surface and compute its basis of holomorphic forms on it. We present numerical examples, recovering known results to test the numerics and giving the yet unknown period m…
We analyze the daily stock data of the Nasdaq Composite index in the 22-year period 1992-2013 and identify market states as clusters of correlation matrices with similar correlation structures. We investigate the stability of the correlation structure of each state by estimating the statistical fluctuations of correlat…
We study the dynamic evolution of cross-correlations in the Chinese stock market mainly based on the random matrix theory (RMT). The correlation matrices constructed from the return series of 367 A-share stocks traded on the Shanghai Stock Exchange from January 4, 1999 to December 30, 2011 are calculated over a moving …
We analyze cross-correlations between price fluctuations of different stocks using methods of random matrix theory (RMT). Using two large databases, we calculate cross-correlation matrices C of returns constructed from (i) 30-min returns of 1000 US stocks for the 2-yr period 1994--95 (ii) 30-min returns of 881 US stock…
New method separates market motion from stock correlations.
Study of WKB asymptotics of Stokes matrices and spectral curves, proving rhombus inequalities.
Study nilpotent Higgs bundles and Calabi-Yau moduli metrics.
Constructs coordinates to diagonalize Toda flow on matrices with simple spectrum.
Study the Mexican stock market's interdependency structure from 2000-2019.
Using data from world stock exchange indices prior to and during periods of global financial crises, clusters and networks of indices are built for different thresholds and diverse periods of time, so that it is then possible to analyze how clusters are formed according to correlations among indices and how they evolve…
In the present paper, we derive a closed-form solution of the multi-period portfolio choice problem for a quadratic utility function with and without a riskless asset. All results are derived under weak conditions on the asset returns. No assumption on the correlation structure between different time points is needed a…
In this paper we derive the exact solution of the multi-period portfolio choice problem for an exponential utility function under return predictability. It is assumed that the asset returns depend on predictable variables and that the joint random process of the asset returns and the predictable variables follow a vect…
Portfolio allocation and risk management make use of correlation matrices and heavily rely on the choice of a proper correlation matrix to be used. In this regard, one important question is related to the choice of the proper sample period to be used to estimate a stable correlation matrix. This paper addresses this qu…
We describe a method to compute the norm on the cotangent space to the moduli space of Riemann surfaces associated to the Finsler Teichmüller metric. Our method involves computing the periods of abelian double covers and is easy to implement for Riemann surfaces presented as algebraic curves using existing tools for ap…
Firms having similar business activities are correlated. We analyze two different cross-correlation matrices C constructed from (i) 30-min price fluctuations of 1000 US stocks for the 2-year period 1994-95 and (ii) 1-day price fluctuations of 422 US stocks for the 35-year period 1962-96. We find that the eigenvectors o…
We introduce a simple approach for testing the reliability of homogeneous generators and the Markov property of the stochastic processes underlying empirical time series of credit ratings. We analyze open access data provided by Moody's and show that the validity of these assumptions - existence of a homogeneous genera…
We detail the theory of Discrete Riemann Surfaces. It takes place on a cellular decomposition of a surface, together with its Poincaré dual, equipped with a discrete conformal structure. A lot of theorems of the continuous theory follow through to the discrete case, we define the discrete analogs of period matrices, Ri…
The difficulty of classification affects the weight matrices' heavy tail appearance in deep learning networks.
We have introduce a new vision of stochastic processes through the geometry induced by the dilation. The dilation matrices of a given processes are obtained by a composition of rotations matrices, contain the measure information in a condensed way. Particularly interesting is the fact that the obtention of dilation mat…
Quantum GBS boosts asset clustering for robust statistical arbitrage portfolios.
We investigate serial correlation, periodic, aperiodic and scaling behaviour of eigenmodes, i.e. daily price fluctuation time-series derived from eigenvectors, of correlation matrices of shares listed on the Johannesburg Stock Exchange (JSE) from January 1993 to December 2002. Periodic, or calendar, components are dete…
We study the energy distribution of harmonic 1-forms on a compact hyperbolic Riemann surface where a short closed geodesic is pinched. If the geodesic separates the surface into two parts, then the Jacobian torus of develops into a torus that splits. If the geodesic is nonseparating then the Jacobian torus of $…
Bayesian method for dynamic correlation matrices improves accuracy and responsiveness.
ButterflyFlow uses butterfly matrices for efficient invertible layers in normalizing flows.
Clusters of financial market states identified over 2006-2019.
We present a brief overview of random matrix theory (RMT) with the objectives of highlighting the computational results and applications in financial markets as complex systems. An oft-encountered problem in computational finance is the choice of an appropriate epoch over which the empirical cross-correlation return ma…
A new method for efficiently updating large-scale matrices in real-time.
Hybrid ResNet and RMT improve covariance matrix estimation for cryptocurrency portfolios.
Unified model for tensor completion using low-rank and sparse Tucker decomposition.
We use methods of random matrix theory to analyze the cross-correlation matrix C of price changes of the largest 1000 US stocks for the 2-year period 1994-95. We find that the statistics of most of the eigenvalues in the spectrum of C agree with the predictions of random matrix theory, but there are deviations for a fe…
Study Bergman kernel metrics on degenerating hyperelliptic surfaces.
Study uses neural networks to filter financial spillovers from noise.
GeoHNN models physics laws for stable, accurate predictions.
We consider random vectors drawn from a multivariate normal distribution and compute the sample statistics in the presence of non-stationary correlations. For this purpose, we construct an ensemble of random correlation matrices and average the normal distribution over this ensemble. The resulting distribution contains…
Spinor formalism is the formalism induced by solutions of the Clifford equation (the connecting operators). For the space-time manifold (n = 4), these operators, connecting the tangent and spinor bundle, are operators that are represented by the Dirac matrices in the special basis. Reduced connecting operators are repr…
We simplify matrix computations for block matrices, especially useful for covariance and correlation matrices.
Minimal submanifolds in matrix spaces proven for specific ranks.
This work employs some techniques in order to filter random noise from the information provided by minimum spanning trees obtained from the correlation matrices of international stock market indices prior to and during times of crisis. The first technique establishes a threshold above which connections are considered a…
Computes isotropy subgroups of orthogonal matrices acting on Hermitian matrices.
Study reveals risk transmission channels among Chinese sectors.
Study on random matrices in deep neural networks with IID entries.