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.
Enhances gradient estimates for Hermitian Monge-Ampère equations.
Derives a general derivative identity for conditional mean in Gaussian noise.
Third-order symmetric Lorentzian manifolds, i.e. Lorentzian manifold with zero third derivative of the curvature tensor, are classified. These manifolds are exhausted by a special type of pp-waves, they generalize Cahen-Wallach spaces and second-order symmetric Lorentzian spaces.
The paper provides estimates for higher-order Ricci curvature along Kähler-Ricci flows.
In the third part of this series we introduce consistent relative value measures for CDS-Bond basis trades using the bond-implied CDS term structure derived from fitted survival rate curves. We explain why this measure is better than the traditionally used Z-spread or Libor OAS and offer simplified hedging and trading …
The unique third-order invariant variational equation in three-dimensional (pseudo)Euclidean space is derived.
Many problems on signal processing reduce to nonparametric function estimation. We propose a new methodology, piecewise convex fitting (PCF), and give a two-stage adaptive estimate. In the first stage, the number and location of the change points is estimated using strong smoothing. In the second stage, a constrained s…
Mathisson's 'new mechanics' of a relativistic spinning particle is shown to follow, in the case of planar motion, from only general requirements of relativistic invariance and of the dependence on third order derivatives along with the 'variationality' feature. The Hamiltonian counterpart ultimately recovers the Dixon …
The task of calibration is to retrospectively adjust the outputs from a machine learning model to provide better probability estimates on the target variable. While calibration has been investigated thoroughly in classification, it has not yet been well-established for regression tasks. This paper considers the problem…
We discuss the probabilistic properties of the variation based third and fourth moments of financial returns as estimators of the actual moments of the return distributions. The moment variations are defined under non-parametric assumptions with quadratic variation method but for the computational tractability, we use …
We discuss a short-time existence theorem of solutions to the initial value problem for a third order dispersive flow for closed curves into a compact almost Hermitian manifold. Our equations geometrically generalize a physical model describing the motion of vortex filament. The classical energy method cannot work for …
In this sequel we extend the derivation of the third order helicity to magnetic fields supported on unlinked domains in 3-space. The formula is expressed in terms of generators of the deRham cohomology of the configuration space of three points in , which is a more practical domain from the perspective of applica…
Paper improves Fisher information estimation methods.
Let E be the Engel group and D be a rank 2 bracket generating left invariant distribution with a Lorentzian metric, which is a nondegenerate metric of index 1. In this paper, we first prove that timelike normal extremals are locally maximizing. Second, we obtain a parametrization of timelike, spacelike, lightlike norma…
New method computes affine normal directions efficiently for sparse polynomials.
A dynamical system on the total space of the fibre bundle of second order accelerations, , is defined as a third order vector field on , called semispray, which is mapped by the second order tangent structure into one of the Liouville vector field. For a regular Lagrangian of second order we prove that …
This note treats the notion of Lagrange derivative for the third order mechanics in the context of covariant Riemannian geometry. The variational differential equation for geodesic circles in two dimensions is obtained. The influence of the curvature tensor on the Lagrange derivative leads to the emergence of the notio…
Equity risk premium is a central component of every risk and return model in finance and a key input to estimate costs of equity and capital in both corporate finance and valuation. An article by Damodaran examines three broad approaches for estimating the equity risk premium. The first is survey based, it consists in …
The paper analyzes the efficiency of gradient estimation methods in noisy function evaluations.
We propose a simple method to produce quandle cocycles from group cocycles, as a modification of Inoue-Kabaya chain map. We further show that, in respect to "universal central extended quandles", the chain map induces an isomorphism between their third homologies. For example, all Mochizuki's quandle 3-cocycles are sho…
We study a sparse negative binomial regression (NBR) for count data by showing the non-asymptotic advantages of using the elastic-net estimator. Two types of oracle inequalities are derived for the NBR's elastic-net estimates by using the Compatibility Factor Condition and the Stabil Condition. The second type of oracl…
New Langevin method achieves third order convergence for strongly log-concave distributions.
Empirical study on long-term discount rates using historical bond prices.
Solves C^3 null gluing problem for Einstein vacuum equations.
We lay theoretical foundations for new database release mechanisms that allow third-parties to construct consistent estimators of population statistics, while ensuring that the privacy of each individual contributing to the database is protected. The proposed framework rests on two main ideas. First, releasing (an esti…
TOLD++ improves convergence of diffusion models by critically damping the forward transition matrix.
We consider the problem of learning a dictionary matrix from a number of observed signals, which are assumed to be generated via a linear model with a common underlying dictionary. In particular, we derive lower bounds on the minimum achievable worst case mean squared error (MSE), regardless of computational complexity…
This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models---including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation---which exploits a certain tensor structure in their low-order observable moments (typically…
We describe various properties and give several characterizations of ternary groups satisfying two axioms derived from the third Reidemeister move in knot theory. Using special attributes of such ternary groups, such as semi-commutativity, we construct a ternary invariant of curves immersed in compact surfaces, conside…
The field of multiple view geometry has seen tremendous progress in reconstruction and calibration due to methods for extracting reliable point features and key developments in projective geometry. Point features, however, are not available in certain applications and result in unstructured point cloud reconstructions.…
Three situations in which filtering theory is used in mathematical finance are illustrated at different levels of detail. The three problems originate from the following different works: 1) On estimating the stochastic volatility model from observed bilateral exchange rate news, by R. Mahieu, and P. Schotman; 2) A stat…
It is studied a 3-dimensional Riemannian manifold equipped with a tensor structure of type (1,1), whose third power is the identity. This structure has a circulant matrix with respect to some basis, i.e. the structure is circulant. On such a manifold a fundamental tensor by the metric and by the covariant derivative of…
Paper develops robust Bayesian models for linear regression under adversarial perturbations.
The conservation laws of the third order quasilinear scalar evolution equations are considered via differential system and characteristic cohomology. We find a subspace of 2 forms in the infinite prolonged space in which every conservation law has a unique representative. The structure of this subspace naturally gives …
This is the third in a series of papers on the geometry and analysis of singular area minimizing hypersurfaces. We show how to derive obstruction and structure theories for scalar curvature constraints without imposing dimensional or topological restrictions on the underlying manifold. To this end, we use skin structur…
New derivation shows how a three-factor learning rule is derived from Oja's rule.
We develop a novel stress-test framework to monitor systemic risk in financial systems. The modular structure of the framework allows to accommodate for a variety of shock scenarios, methods to estimate interbank exposures and mechanisms of distress propagation. The main features are as follows. First, the framework al…
We define homology of ternary algebras satisfying axioms derived from particle scattering or, equivalently, from the third Reidemeister move. We show that ternary quasigroups satisfying these axioms appear naturally in invariants of Reidemeister, Yoshikawa, and Roseman moves. Our homology has a degenerate subcomplex. T…
In this paper we introduce an efficient fat-tail measurement framework that is based on the conditional second moments. We construct a goodness-of-fit statistic that has a direct interpretation and can be used to assess the impact of fat-tails on central data conditional dispersion. Next, we show how to use this framew…
In the tensor completion problem, one seeks to estimate a low-rank tensor based on a random sample of revealed entries. In terms of the required sample size, earlier work revealed a large gap between estimation with unbounded computational resources (using, for instance, tensor nuclear norm minimization) and polynomial…
The paper studies third-order PDEs invariant under affine transformations and connects them to the Fubini-Pick invariant.
We compute the characteristic Cartan connection associated with a system of third order ODEs. Our connection is different from Tanaka normal one, but still is uniquely associated with the system of third order ODEs. This allows us to find all fundamental invariants of a system of third order ODEs and, in particular, de…
The paper studies steady motions of fibre-reinforced fluids on curved surfaces.
The study finds conditions for a third rank Killing tensor field on a 2D Riemannian torus.
The atomic swap protocol allows for the exchange of cryptocurrencies on different blockchains without the need to trust a third-party. However, market participants who desire to hold derivative assets such as options or futures would also benefit from trustless exchange. In this paper I propose the atomic swaption, whi…
In this paper we present the solution to a longstanding problem of differential geometry: Lie's third theorem for Lie algebroids. We show that the integrability problem is controlled by two computable obstructions. As applications we derive, explain and improve the known integrability results, we establish integrabilit…
Paper calculates third coefficient in Kaehler-Einstein metric expansion.
A third-order approximation for close-to-the-money European option prices under an infinite-variation CGMY Lévy model is derived, and is then extended to a model with an additional independent Brownian component. The asymptotic regime considered, in which the strike is made to converge to the spot stock price as the ma…