GASC models semantic change in Ancient Greek texts using genre metadata.
problem Associating correct meanings in historical Ancient Greek texts.
method Develops a dynamic semantic change model leveraging genre metadata.
result Improves predictive performance on semantic change in Ancient Greek texts.
A new method for computing Greeks without bias, improving stability.
problem Inaccurate and unstable computation of second order Greeks (like Gamma) in financial instruments.
method Apply Chebyshev interpolation techniques to finite differences for improved stability.
result Improved stability and accuracy in computing spot Greeks without bias.
Fourier methods fail to accurately approximate option Greeks in realistic market conditions.
problem Failure of Fourier pricing techniques to approximate Greeks in realistic market parameters.
method Used Fourier techniques like Carr-Madan formula, COS method, and Lewis formula to approximate Greeks, which failed in some market conditions.
result Empirically showed that Fourier methods completely fail to approximate Greeks in realistic market environments.
The computation of Greeks for exponential Lévy models are usually approached by Malliavin Calculus and other methods, as the Likelihood Ratio and the finite difference method. In this paper we obtain exact formulas for Greeks of European options based on the Lewis formula for the option value. Therefore, it is possible…
Quasi-Monte Carlo speeds up option Greeks calculation on GPUs.
problem Efficiently calculating option Greeks for risk management.
method Quasi-Monte Carlo (QMC) combined with GPU acceleration for pathwise sensitivity calculation.
result Increased computational speed and efficiency in estimating option Greeks.
Researchers compute Greeks for rough Volterra SV models using Malliavin calculus.
problem Computing Greeks under rough Volterra stochastic volatility models.
method Malliavin calculus techniques, extending integration by parts to non-square integrable functionals.
result Formulas for computing Greeks (Delta, Gamma, Rho, Vega) under various rough Volterra SV models.
Matrix approximation method for Bachelier option pricing and Greeks under stochastic volatility models
problem Computing option prices and Greeks for stochastic volatility models
method Matrix approximation using elementary linear algebra
result Option prices and Greeks computed for infinitely many strikes with a finite number of expectations
New method reduces Monte Carlo error in option pricing and Greeks estimation.
problem Reducing Monte Carlo error in option pricing and Greeks estimation.
method Denoised Monte Carlo technique for LSV models.
result Reduces Monte Carlo error by an order of magnitude.
Ancient curve flows classified into specific types.
problem Classifying ancient finite-entropy curve shortening flows.
method Proving flow types through mathematical analysis.
result Ancient flows are one of several specific types.
The aim of the present article is to treat the Greek public debt issue strictly as a curve fitting problem. Thus, based on Eurostat data and using the Mathematica technical computing software, an exponential function that best fits the data is determined modelling how the Greek public debt expands with time. Exploring …
Ancient solutions to mean curvature flow have unique shapes.
problem Understanding unique shapes of ancient solutions.
method Proved a Bernstein theorem for ancient solutions.
result Ancient solutions to mean curvature flow have unique shapes.
Study on ancient Ricci flows with positive curvature, proving noncollapsedness.
problem Characterizing ancient Ricci flows with positive sectional curvature.
method Analyzing complete and noncompact Type I ancient Ricci flows with positive sectional curvature.
result Ancient solutions are noncollapsed on all scales in complete and noncompact cases, and in even-dimensional closed cases.
The paper uses 3D shapes to reveal sundial design adjustments based on latitude.
problem Identifying sundial design adjustments based on installation location.
method Shape analysis in a high-dimensional space, regression in shape space.
result Sundial design adjustments were latitude-dependent.
Ancient pancakes solve mean curvature flow problem.
problem Mean curvature flow problem
method Constructing an embedded ancient solution as a stack of pancakes
result Embedded ancient solution to mean curvature flow
Ancient solutions to Ricci flow in higher dimensions are mostly cylinders or solitons.
problem Uniqueness of ancient κ-solutions in higher dimensions. method Analysis of ancient κ-solutions with specific properties. result The only noncompact ancient κ-solutions are cylinders, quotients, or the Bryant soliton. Ancient solutions on a strip are constant if polynomial, and have finite-dimensional space for slower growth.
problem Characterizing ancient solutions on an infinite strip with polynomial and exponential growth.
method Analyzing parabolic equations on an infinite strip, proving properties of ancient solutions.
result Ancient solutions on the strip are constant if they grow polynomially, and have a finite-dimensional space for slower exponential growth.
Let n≥3 and m=n+2n−2. We construct 5-parameters, 4-parameters, 3-parameters ancient solutions of the equation vt=(vm)xx+v−vm, v>0, in R×(−∞,T) for some T∈R. This equation arises in the study of Yamabe flow. We obtain various properties of the ancient so…
Ancient Ricci flow found from Taub-Bolt metric.
problem Existence of ancient Ricci flow solutions.
method Analysis of Ricci flow from Taub-Bolt metric.
result Non-trivial ancient solution to Ricci flow found.
Ancient curves span halfplanes via flow.
problem Ancient solutions to Curve Shortening Flow.
method Constructing infinite family of solutions.
result Spanning halfplane with ancient curves.
Classifies ancient flows in a disc with boundary.
problem Ancient convex flows in a disc with boundary.
method Classifies flows using curve shortening.
result Ancient convex flows in a disc are classified.
Ancient solutions to heat equations on graphs are shown to be analytic in time.
problem Analyzing the analyticity of ancient solutions to heat equations on graphs.
method Proving time analyticity under a sharp growth condition.
result Ancient solutions to heat equations on graphs are time analytic under certain conditions.
Classifies ancient convex curves in convex domains.
problem Ancient convex curve shortening flows on convex domains.
method Classification of convex ancient solutions.
result Ancient convex curves in convex domains classified.
Ancient solutions to Kähler Ricci flow classified completely.
problem Ancient solutions to Kähler Ricci flow with nonnegative bisectional curvature.
method Complete classification of κ-noncollapsed, complete ancient solutions.
result Classification of all ancient solutions to Kähler Ricci flow with nonnegative bisectional curvature.
Paper classifies ancient solutions to 3D Ricci flow.
problem Classifying ancient solutions to 3D Ricci flow.
method Proves uniqueness of solutions based on classification criteria.
result Ancient solutions are either shrinking spheres or Perelman's Type II solutions.
Ancient symplectic solutions to mean curvature flow are flat.
problem Understanding ancient solutions to mean curvature flow in symplectic geometry.
method Using a complex phase map to prove a Bernstein theorem.
result Ancient solutions to the symplectic mean curvature flow are flat.
Ancient solutions to biharmonic heat equation bounded by polynomial dimensions.
problem Bounding ancient solutions to biharmonic heat equation.
method Using polynomial volume growth and dimensions of biharmonic functions.
result Ancient solutions are bounded by polynomial dimensions.
Ancient Ricci flows are identified without curvature sign condition.
problem Identifying type II ancient Ricci flows and their backward limits.
method Using a size condition of the sharp log Sobolev functional near infinity.
result Rigidity result for ancient Ricci flows without sign condition on curvatures.
The paper constructs ancient solutions to curvature flows in bounded and unbounded regions.
problem Understanding ancient solutions to curvature flows in bounded and unbounded regions.
method Constructing pancake-like and sausage-like ancient compact solutions.
result Ancient solutions to curvature flows in bounded and unbounded regions.
A new method computes Greeks for multi-asset options using tensor trains and Fourier transforms.
problem Efficient computation of Greeks for multi-asset options with high accuracy and low sample complexity.
method Tensor train (TT) representations of Fourier-based pricing functions, combined with numerical differentiation or analytical approaches.
result Significant speed-ups of up to 105imes over Monte Carlo simulations while maintaining comparable accuracy. Study ancient solutions to free boundary mean curvature flow in convex manifolds.
problem Understanding ancient solutions to free boundary mean curvature flow in convex manifolds.
method Establish rigidity results and construct foliations to describe ancient solutions.
result Ancient solutions to free boundary mean curvature flow are rigid and exhaust all possibilities under certain conditions.
Ancient flows of elliptic functionals classified in various dimensions.
problem Classifying ancient solutions to gradient flows of elliptic functionals.
method Analyzing closed ancient solutions in Riemannian manifolds.
result Ancient solutions classified in multiple dimensions and cases.
New ancient solutions found for curvature flow in 2D.
problem Ancient solutions for curvature flow in 2D.
method Constructing and classifying convex ancient solutions.
result All convex ancient solutions classified for α∈(32,1). Ancient flows by curvature powers in 2D have finite entropy.
problem Existence of non-homothetic ancient flows by powers of curvature in R2. method Determined Morse indices and kernels of the linearized operator of shrinkers. Constructed flows using unstable eigenfunctions.
result Existence of ancient flows with finite entropy.
Study ancient Ricci flow solutions, proving unique asymptotic behavior.
problem Understanding unique asymptotics of compact ancient solutions to 3D Ricci flow.
method Analyzing noncollapsed compact ancient solutions, proving asymptotic behavior.
result Proves unique asymptotic behavior for compact ancient solutions.
New ancient solutions to mean curvature flow in high dimensions identified.
problem Finding ancient solutions to mean curvature flow in high codimension.
method Constructing compact ancient solutions to mean curvature flow in Euclidean space with high codimension.
result Characterization of the asymptotic behavior of constructed ancient solutions.
Ancient solutions of Ricci flow with Type I growth are classified.
problem Understanding ancient solutions of Ricci flow with specific curvature growth.
method Analyzing ancient solutions with Type I curvature growth in arbitrary dimensions.
result Ancient solutions with Type I growth are classified into specific types.
This paper presents a new methodology to compute first-order Greeks for barrier options under the framework of path-dependent payoff functions with European, Lookback, or Asian type and with time-dependent trigger levels. In particular, we develop chain rules for Wiener path integrals between two curves that arise in t…
New ancient curve shortening flows created from grim reapers.
problem Ancient curve shortening flows in 3D space.
method Built from translating grim reapers in perpendicular planes.
result Constructed new nonplanar ancient solutions.
Ancient mean curvature flows get codimension bounds from their tangent flow.
problem Understanding the limiting behavior of ancient mean curvature flows.
method Proving codimension bounds using the tangent flow at −∞. result Ancient mean curvature flows are rigid to their tangent flow at −∞. Study ancient caloric functions on graphs, extending a theorem from manifolds.
problem Bounding the dimension of ancient caloric functions on graphs.
method Extending Colding and Minicozzi's theorem to graphs.
result Dimension of ancient caloric functions is bounded by growth degree and graph dimension.
Ancient pancake solutions found for curvature flows.
problem Finding unique ancient solutions to curvature flows.
method Constructing and analyzing O(1)imesO(n)-invariant ancient solutions. result Unique O(n)-invariant ancient solutions found. Ancient solutions in 3D are mostly cylinders or symmetric.
problem Understanding the structure of ancient solutions to the Ricci flow in 3D.
method Detailed proof of compact ancient κ-solutions being rotationally symmetric.
result Compact ancient κ-solutions are rotationally symmetric.
Ancient solutions found for mean curvature flow of isoparametric submanifolds.
problem Mean curvature flow of isoparametric submanifolds in Euclidean spaces and spheres.
method Showed all solutions are ancient solutions and discussed rigidity.
result All ancient solutions found for isoparametric submanifolds in Euclidean spaces and spheres.
Classifies ancient ovals in higher dimensional mean curvature flow.
problem Classifying ancient ovals in higher dimensional mean curvature flow.
method Spectral parametrization to classify k-ovals.
result Classifies k-ovals in arbitrary dimensions.
We consider an embedded convex ancient solution Γt to the curve shortening flow in R2. We prove that there are only two possibilities: the family Γt is either the family of contracting circles, which is a type I ancient solution, or the family of evolving Angenent ovals, which correspond to a type II …
Study ancient Ricci flows with nonnegative Ricci curvature and their asymptotic geometry.
problem Understanding the asymptotic geometry of ancient Ricci flows with nonnegative Ricci curvature.
method Analyze tangent flows at infinity and use estimates for noncollapsed F-limit metric solitons.
result Two dichotomy theorems for ancient Ricci flows: either the asymptotic volume ratio is zero or every tangent flow is a Ricci flat cone.
Dupire's functional Itô calculus provides an alternative approach to the classical Malliavin calculus for the computation of sensitivities, also called Greeks, of path-dependent derivatives prices. In this paper, we introduce a measure of path-dependence of functionals within the functional Itô calculus framework. Name…
Proves rigidity of ancient solutions in mean curvature flow.
problem Rigidity of ancient solutions in mean curvature flow.
method Point-wise estimate for second fundamental form.
result Rigidity theorem of ancient solutions in codimension one.