Defines risk-free portfolios and risk-free rate using gauge symmetries.
problem Identifying a consistent definition of risk-free rate in economics.
method Introduces three gauge invariant differential operators to define risk-free portfolios and identifies the risk-free rate as the return of an infinitely diversified portfolio.
result Identifies the risk-free rate as the return of an infinitely diversified portfolio and connects it to global price rescaling as a gauge symmetry.
Adaptive method improves prediction intervals with global coverage guarantees and local error distribution.
problem Global coverage guarantees of conformal regression are often violated by local error distributions.
method Adaptive Conformal Regression with Jackknife+ Rescaled Scores
result Improves local coverage without sacrificing global coverage, especially in low-data regimes.
We report an empirical study of Tehran Price Index (TEPIX). To analyze our data we use various methods like as, rescaled range analysis (R/S), modified rescaled range analysis (Lo's method), Detrended Fluctuation Analysis (DFA) and generalized Hurst exponents analysis. Based on numerical results, the scaling range of…
We develop a ``canonical Wick rotation-rescaling theory in 3-dimensional gravity''. This includes: (a) A simultaneous classification that shows how generic maximal globally hyperbolic spacetimes of constant curvature, which admit a complete Cauchy surface (in particular a compact one), as well as complex projective str…
Rescaled ASGD optimizes distributed learning under heterogeneous data.
problem Vanilla ASGD biases towards a frequency-weighted average of local objectives.
method Rescale worker stepsizes by their computation times.
result Rescaled ASGD converges to the correct global objective in fixed-computation model.
Study Chen's flow of curves in two settings: closed circles and lines, identifying geometric conditions for global behavior.
problem Understanding the global behavior of Chen's flow of curves in two settings.
method Investigated two settings: closed immersed ω-circles and immersed lines with a cocompactness condition. Analyzed geometric conditions and curvature effects.
result Identified conditions ensuring the flow shrinks every initial curve to a point, including a rescaling method.
Study on stability of cylindrical singularities in MCF of finite codimensions.
problem Stability of cylindrical singularities in mean curvature flow.
method Construction of stable manifold, explicit solutions, asymptotic analysis.
result Asymptotic stability of cylindrical singularities under generic perturbations.
The classical Getzler rescaling theorem is extended to the transverse geometry of foliations. More precisely, a Getzler rescaling calculus, as well as a Block-Fox calculus of asymptotic operators, is constructed for all transversely spin foliations. This calculus applies to operators of degree m globally times degree…
"Ends of hyperbolic 3-manifolds should support canonical Wick Rotations, so they realize effective interactions of their ending globally hyperbolic spacetimes of constant curvature." We develop a consistent sector of WR-rescaling theory in 3D gravity, that, in particular, concretizes the above guess for many geometrica…
We report on the occurrence of an anomaly in the price impacts of small transaction volumes following a change in the fee structure of an electronic market. We first review evidence for the existence of a master curve for price impact on the Johannesburg Stock Exchange (JSE). On attempting to re-estimate a master curve…
We study the average price impact of a single trade executed in the NYSE. After appropriate averaging and rescaling, the data for the 1000 most highly capitalized stocks collapse onto a single function, giving average price shift as a function of trade size. This function increases as a power that is the order of 1/2 f…
Algorithm optimizes functions without parameters, converging to global minima.
problem Optimizing functions without parameters.
method Follow The Regularized Leader with rescaled gradients and time-varying regularizers.
result Converges to global minimizer for variationally coherent functions.
This work justifies neural collapse under MSE loss and analyzes the optimization landscape.
problem Understanding neural collapse in deep neural networks under MSE loss.
method Global landscape analysis of vanilla nonconvex MSE loss.
result The only global minimizers are neural collapse solutions.
The aim of this survey is to give an overview on the geometry of Einstein maximal globally hyperbolic 2+1 spacetimes of arbitrary curvature, conatining a complete Cauchy surface of finite type. In particular a specialization to the finite type case of the canonicla Wick rotation-rescaling theory, previously developed b…
We study Vanna-Volga methods which are used to price first generation exotic options in the Foreign Exchange market. They are based on a rescaling of the correction to the Black-Scholes price through the so-called `probability of survival' and the `expected first exit time'. Since the methods rely heavily on the approp…
Deriving option prices from operational-time Markov lattices
problem Option pricing
method Operational-time Markov lattice
result Derives option-pricing equations from an operational-time Markov lattice
Motivated by the desire to bridge the gap between the microscopic description of price formation (agent-based modeling) and the stochastic differential equations approach used classically to describe price evolution at macroscopic time scales, we present a mathematical study of the order book as a multidimensional cont…
Proves convergence of mean curvature flow on cylinders with unique continuation.
problem Understanding the convergence and uniqueness of mean curvature flow on cylindrical surfaces.
method Proves convergence and provides unique continuation results for mean curvature flow on cylinders.
result Proves that rescaled mean curvature flow on cylinders converging super-exponentially must coincide with the cylinder itself.
Let V be a maximal globally hyperbolic flat n+1--dimensional space--time with compact Cauchy surface of hyperbolic type. We prove that V is globally foliated by constant mean curvature hypersurfaces Mτ, with mean curvature τ taking all values in (−∞,0). For n≥3, define the rescaled volume of $…
Study on small-time behavior of rough Bergomi model using large deviations principle.
problem Understanding the small-time behavior of the rough Bergomi model.
method Proved a large deviations principle for a rescaled log stock price process.
result Characterized the small-time behavior of the implied volatility.
The study approximates option prices using Hermite polynomials without assuming a specific distribution.
problem Approximating option prices without assuming a specific distribution of returns.
method Approximating the logarithmic return's density by a linear combination of rescaled Hermite polynomials.
result Empirical results suggest reasonable performance for options with moderate strike prices.
We present a general Markovian framework for order book modeling. Through our approach, we aim at providing a tool enabling to get a better understanding of the price formation process and of the link between microscopic and macroscopic features of financial assets. To do so, we propose a new method of order book repre…
In this short notes, we discuss monotonicity formulas under various rescaled versions of Ricci flow. The main result is Theorem \ref{theo rescaled}.
The paper calculates spectral torsion for rescaled Dirac operators on manifolds.
problem Computing spectral torsion for rescaled Dirac operators.
method Using trilinear Clifford multiplication and functional of differential one-forms.
result Computed spectral torsion for four types of rescaled Dirac operators.
New spectral torsion defined for rescaled Dirac operators.
problem Defining spectral torsion for rescaled Dirac operators.
method Using three vector fields and noncommutative residue.
result Computed spectral torsion for one form rescaled Dirac operators.
For a Riemannian manifold M, we determine some curvature properties of a tangent bundle equipped with the rescaled metric.The main aim of this paper is to give explicit formulae for the rescaled metric on TM, and investigate the geodesics on the tangent bundle with respect to the rescaled Sasaki metric.
Study shows how heavy-tailed Hawkes processes can model rough volatility in financial markets.
problem Modeling rough volatility in financial markets with heavy-tailed Hawkes processes.
method Established weak convergence of Hawkes process with power-law kernel, derived scaling limit for financial market model.
result Price-volatility process converges weakly to a rough Heston model after rescaling.
Study geometric characterization of asymptotic pseudodifferential calculus on spinor bundles.
problem Geometric characterization of asymptotic pseudodifferential calculus on spinor bundles.
method Groupoid approach to pseudodifferential calculus, rescaled bundle.
result Rescaled bundle provides geometric characterization to asymptotic pseudodifferential calculus on spinor bundles.
The paper calculates the noncommutative residue for a rescaled Dirac operator on 6D manifolds.
problem Computing the noncommutative residue for a specific Dirac operator on 6D manifolds.
method Calculations and proofs for the rescaled Dirac operator fDh on 6D compact manifolds.
result Proof of the Kastler-Kalau-Walze type theorem for the rescaled Dirac operator on 6D compact manifolds with boundary.
Rescaling expansiveness proven for k*-expansive vector fields.
problem Proving rescaling expansiveness for k*-expansive vector fields.
method Introducing and exploring singular-expansive flows.
result Rescaling expansiveness established for k*-expansive vector fields.
Cryptocurrency forecasting model considers macro, sentiment, and technical indicators.
problem High price volatility in cryptocurrency markets.
method Dual-prediction mechanism incorporating macroeconomic fluctuations, technical indicators, and individual cryptocurrency price changes.
result The proposed model outperforms ten comparison methods in short-term cryptocurrency forecasting.
A new approach simplifies Sliced-Wasserstein distances to improve learning performance.
problem The concentration of measure phenomenon makes random projections uninformative in high dimensions.
method Propose rescaling the 1D Wasserstein distance to make all slices equally informative.
result The classical Sliced-Wasserstein, properly configured, can match or surpass complex variants.
Local index theorem for manifolds with Lie structure at infinity using rescaling and renormalized supertrace.
problem Proving an Atiyah-Singer type index theorem for manifolds with Lie structure at infinity.
method Rescaling technique similar to Getzler's, integrating Lie groupoid, functional calculus, heat kernel expansion, Lichnerowicz theorem.
result Proof of a local index theorem for Dirac operators on Lie manifolds.
Privacy-preserving crypto exchanges adjust prices based on Gaussian noise.
problem Ensuring fair pricing in privacy-preserving cryptocurrency exchanges.
method Derive Kyle equilibrium with Gaussian noise perturbation, rescaling price-impact and strategy factors.
result Identify a privacy subsidy as a transfer from LP pool to traders, invariant to noise.
Fast algorithm for rescaling vectors with clipping, improving training efficiency.
problem Efficiently rescale vectors to a desired length while maintaining them within a domain after clipping.
method Analytical solution for optimal rescaling using fast and differentiable algorithm.
result Optimal rescaling can be found analytically, improving training efficiency for neural networks.
Study Fourier estimator for spot volatility with unbounded coefficients and jumps.
problem Estimating spot volatility with unbounded coefficients and jumps in price process.
method Fourier estimator for spot volatility, convergence analysis for unbounded coefficients and jumps.
result Convergence of trigonometric polynomial to volatility's path, almost sure convergence of reconstructed volatility.
Study uses APT and QR to identify risk factors affecting crude oil returns.
problem Determining the risk factors impacting crude oil returns.
method Employed Arbitrage Pricing Theory and Quantile Regression.
result Identified key risk factors: industrial production, inflation, energy prices, yield curve shape, and economic policy uncertainty.
Our work sheds new light on the role of oil prices in shaping the world economy by investigating flows of goods and services through global value chains between 1960 and 2011, by means of Markov Chain and network analysis. We show that over that time period the international division of labor and trade patterns are tig…
Globalization processes interweave economic structures at a worldwide scale, trade playing a central role as one of the elemental channels of interaction among countries. Despite the significance of such phenomena, measuring economic globalization still remains an open problem. More quantitative treatments could improv…
A new method to rescale ReLU neural networks based on path-lifting.
problem Lack of principled ways to leverage rescaling symmetries in ReLU neural networks.
method Introduces a geometrically motivated criterion to rescale neural network parameters, aligning a kernel in the path-lifting space with a chosen reference.
result Proposed method can speed up training and aligns a kernel in the path-lifting space with a chosen reference.
Paper derives second order approximations for limit order books.
problem Modeling fluctuations in price and volume processes.
method Second order approximation of infinite dimensional limit order book dynamics.
result Confidence intervals for optimal portfolio liquidation models.
High and volatile global food prices have led to food riots and played a critical role in triggering the Arab Spring revolutions in recent years. The severe drought in the US in the summer of 2012 led to a new increase in food prices. Through the fall, they remained at a threshold above which the riots and revolutions …
Theory developed for Hilbert geometry over valued fields, linking real and non-Archimedean geometries.
problem Understanding Hilbert geometry over general valued fields and their limits.
method Developed a theory of Hilbert geometry over general ordered valued fields, proving ultralimit results.
result Ultralimit of rescaled real Hilbert geometries is isometric to a non-Archimedean Hilbert metric space.
This paper tackles non-vacuous generalization bounds in ReLU networks by resolving rescaling invariances.
problem Non-vacuous generalization guarantees for ReLU networks with rescaling invariances.
method Proposes a lifted representation to resolve rescaling invariances and studies KL-based rescaling-invariant PAC-Bayes bounds.
result KL-based rescaling-invariant PAC-Bayes bounds provide tighter guarantees and resolve discrepancies in network complexity.
Localizes Wodzicki residue for logarithm of differential operators.
problem Localizing Wodzicki residue for logarithm of differential operators.
method Localisation formula using rescaled differential operators and spinor bundles.
result Expresses index of Dirac operator in terms of local density involving logarithm.
New Lipschitz bound for ReLU networks resists weight rescaling.
problem Lack of robustness guarantees for ReLU networks under weight perturbations.
method Rescaling-invariant Lipschitz bound based on path-metrics.
result The new bound applies to various ReLU-DAG architectures and resists neuron-wise rescalings.
Proposes a framework to incorporate global sensitivity into local surrogate models.
problem Narrowing focus to local scale in surrogate modeling leads to re-learning global trends.
method Integrates global sensitivity analysis into local surrogate models through input warping.
result Local models become equally sensitive to all input directions, focusing on local dynamics.
We exploit the spinor description of four-dimensional Walker geometry, and conformal rescalings of such, to describe the local geometry of four-dimensional neutral geometries with algebraically degenerate self-dual Weyl curvature and an integrable distribution of alpha-planes (algebraically special real alpha-geometry)…