A new method solves American put options with high accuracy and speed.
problem Solving American put options with high accuracy and speed.
method Adaptive fourth-order Runge-Kutta-Fehlberg method coupled with a fourth-order compact scheme.
result The method provides a more accurate solution and better performance in terms of computational speed.
The study compares differencing methods for financial data and finds fractional differencing improves model performance.
problem Improving financial time series forecasting models using appropriate data transformation techniques.
method Comparative analysis of traditional logarithmic returns and fractional differencing methods, including tempered extensions.
result Fractional differencing methods improve model forecasting performance and trading strategy effectiveness.
In recent years, active subspace methods (ASMs) have become a popular means of performing subspace sensitivity analysis on black-box functions. Naively applied, however, ASMs require gradient evaluations of the target function. In the event of noisy, expensive, or stochastic simulators, evaluating gradients via finite …
Our understanding of reinforcement learning (RL) has been shaped by theoretical and empirical results that were obtained decades ago using tabular representations and linear function approximators. These results suggest that RL methods that use temporal differencing (TD) are superior to direct Monte Carlo estimation (M…
Long and short memory in economic processes is usually described by the so-called discrete fractional differencing and fractional integration. We prove that the discrete fractional differencing and integration are the Grunwald-Letnikov fractional differences of non-integer order d. Equations of ARIMA(p,d,q) and ARFIMA(…
We develop methods to approximate derivatives for causal inference problems using data.
problem Estimating causal effects from data when distributions are not known.
method Constructive algorithm approximating Gateaux derivatives via finite differencing.
result Derives conditions for finite-difference approximations to preserve statistical benefits.
A fast, accurate method for pricing American options with free boundaries.
problem Pricing American options with free boundaries efficiently and accurately.
method A sixth-order compact finite difference scheme with a dynamic staggered boundary scheme and 3(2) R-K Bogacki-Shampine time stepping.
result An efficient sixth-order compact scheme for pricing American options with free boundaries.
We study singularity formation in spherically symmetric solutions of the charge-one and charge-two sector of the (2+1)-dimensional S^2 sigma-model and the (4+1)-dimensional Yang-Mills model, near the adiabatic limit. These equations are non-integrable, and so studies are performed numerically on rotationally symmetric …
New method combines long-memory reservoirs for accurate dengue forecasting from short data.
problem Accurate dengue forecasting from short, noisy, non-stationary, and nonlinear data.
method Fractional ESN and Wavelet ESN frameworks integrating long-term memory.
result fESN and wESN outperform baselines in multiple dengue datasets and forecasting horizons.
In this short report, we investigate the ability of the DCCA coefficient to measure correlation level between non-stationary series. Based on a wide Monte Carlo simulation study, we show that the DCCA coefficient can estimate the correlation coefficient accurately regardless the strength of non-stationarity (measured b…
This study uses moving average cluster entropy to analyze financial market dynamics.
problem Understanding long-range dependence in financial markets.
method Moving average cluster entropy approach applied to ARFIMA and FBM processes.
result Long-range positive correlation in financial markets is linked to the cluster entropy behavior.
Enhanced LSTM predicts equity trends, outperforming traditional methods.
problem Nonstationary and nonlinear market regimes challenge trend forecasting.
method LSTM-based framework for forecasting equity trend differences.
result LSTM framework outperforms traditional methods in terms of overall PNL.
Study forecasts U.S. bond index using deep learning, finding persistence is key.
problem Forecasting U.S. aggregate bond index with deep learning methods.
method Constructed a stationary but maximally persistent representation of the bond index, evaluated using MLPs and CNNs.
result Deep learning models outperform traditional methods in short-horizon forecasting of bond indices.
Online learning rbfnet improves multi-horizon returns forecasts for financial time series.
problem Nonstationarity and concept drift in financial time series.
method Combines feature representation transfer with sequential optimisation.
result Online learning rbfnet outperforms random-walk and batch learners.
NoTMF forecasts sparse urban road movement speeds with nonstationary temporal matrix factorization.
problem Sparse and nonstationary movement speed data from urban roads.
method Nonstationary Temporal Matrix Factorization (NoTMF) model.
result NoTMF outperforms baseline models in forecasting urban road movement speeds.
Classifies compact spaces by shape, finite spaces by weak homotopy.
problem Classifying compact Hausdorff spaces and finite topological spaces.
method Constructs a category that classifies spaces by shape and weak homotopy.
result Classifies compact spaces by shape, finite spaces by weak homotopy.
The paper explores conditions for compactness and finiteness in stratified homotopy theory.
problem Conditions for compactness and finiteness in stratified homotopy theory.
method Analyzes conditions for compactness and finiteness in stratified homotopy theory, providing sufficient conditions and deducing results.
result Conditions for compactness and finiteness in stratified homotopy theory are established.
Characterizes compact complex surfaces with finite homotopy rank-sum.
problem Compact complex surfaces with finite homotopy rank-sum.
method Characterization and proof of Steinness of universal cover.
result Smooth compact complex Kaehler surfaces with finite homotopy rank-sum.
Finite vector bundles over complex manifolds are trivializable via finite covers.
problem Understanding when holomorphic vector bundles over compact complex manifolds are trivializable.
method Introducing finite bundles and using finite étale covers to trivialize holomorphic vector bundles.
result Holomorphic vector bundles over compact complex manifolds are finite if and only if they admit a flat holomorphic connection with finite monodromy.
Compact curve solution emerges from non-compact curve.
problem Constructing solutions from non-compact curves.
method Slingshot solution to curve shortening flow.
result Compact embedded solution exists for a finite time.
We study compact Riemannian manifolds for which the light between any pair of points is blocked by finitely many point shades. Compact flat Riemannian manifolds are known to have this finite blocking property. We conjecture that amongst compact Riemannian manifolds this finite blocking property characterizes the flat m…
New method for pricing options in stochastic volatility models.
problem Pricing options in models with stochastic volatility.
method Time-adaptive, high-order compact finite difference scheme.
result Extends fourth-order multistep methods to stochastic volatility models.
Study compares and unifies finiteness properties of locally compact groups.
problem Understanding finiteness properties of locally compact groups.
method Comparing and unifying three families of finiteness properties: type Cn, coarse (n−1)-connectedness, and type Fn. result All three families lead to the same notion for locally compact groups.
New method reduces variance in random coordinate descent for Langevin Monte Carlo.
problem Efficient sampling from log-concave distributions in high dimensions.
method Introduces RCAD, a variance reduction technique for RCD-LMC.
result RCAD-O-LMC and RCAD-U-LMC converge within the same number of iterations as classical LMC methods, saving computational cost.
We prove the following theorem for Holomorphic Foliations in compact complex kaehler manifolds: if there is a compact leaf with finite holonomy, then every leaf is compact with finite holonomy. As corollary we reobtain stability theorems for compact foliations in Kaehler manifolds of Edwards-Millett-Sullivan and Hollma…
Survey of recent results on homogeneous finite-dimensional spaces.
problem Understanding properties of homogeneous finite-dimensional spaces.
method Discussion of recent results and unsolved problems.
result Discussion of recent results and unsolved problems.
Study on compact and finite-type support in mapping class group homology.
problem Understanding non-trivial classes supported on compact or finite-type subsurfaces.
method Use of shiftable subsurfaces and homological stability for finite-type surfaces.
result Almost-complete answer for surfaces with positive genus, partial answer for zero genus.
Compact manifolds with boundary have finite type mapping class groups.
problem Understanding the structure of mapping class groups for manifolds with boundaries.
method Proved finite type for mapping class groups under specific dimension and connectivity assumptions.
result Mapping class groups of compact manifolds with boundaries are of finite type.
Universal spaces for finite topological spaces simplify shape descriptions.
problem Describing shape properties of compact metric spaces.
method Inverse limits of finite spaces and Alexandroff extensions.
result Universal spaces simplify shape descriptions of compact metric spaces.
We prove a finiteness result for the ∂-patterned guts decomposition of all 3-manifolds obtained by splitting a given orientable, irreducible and ∂-irreducible 3-manifold along a closed incompressible surface. Then using the Thurston norm, we deduce that the JSJ-pieces of all 3-manifolds dominated by a…
Study shows how certain spaces can be mapped to R^n with specific properties.
problem Characterizing and mapping locally compact median spaces of finite rank.
method Analyzing the combinatorics of halfspaces and properties of isometric actions.
result Spaces with certain actions are isometric to R^n, and orbits are discrete.
We evaluate the hedging performance of a high-order compact finite difference scheme from [4] for option pricing in Bates model. We compare the scheme's hedging performance to standard finite difference methods in different examples. We observe that the new scheme outperforms a standard, second-order central finite dif…
We prove there exists a compact embedded minimal surface in a complete finite volume hyperbolic 3-manifold N. We also obtain a least area, incompressible, properly embedded, finite topology, 2-sided surface. We prove a properly embedded minimal surface of bounded curvature has finite topology. This dete…
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.
Compact holonomy groups found in symmetric spaces.
problem Characterizing holonomy groups in symmetric spaces.
method Analyzing the holonomy group structure of locally symmetric spaces.
result Holonomy groups are compact and have finite index in the orthogonal group.
Let G be a finitely generated group having the property that any action of any finite-index subgroup of G by homeomorphisms of the circle must have a finite orbit. (By a theorem of E.Ghys, lattices in simple Lie groups of real rank at least two have this property.) Suppose that such a G acts on a compact manifold M by …
Study entropy bounds and finiteness for symmetric self-shrinkers.
problem Entropy and finiteness of symmetric self-shrinkers.
method Comparison geometry, entropy bounds, compactness theorem.
result Only finitely many symmetric self-shrinkers with extra symmetry.
The study shows a finite number of groups acting on hyperbolic spaces with bounded entropy and compact quotient.
problem Finite number of groups acting on hyperbolic spaces with bounded entropy and compact quotient.
method Analyzing torsion-free groups acting by isometries on hyperbolic metric spaces with bounded entropy and compact quotient.
result The set of such groups is finite and can be estimated based on hyperbolicity constant, entropy, and quotient diameter.
Let H=Δ+V be a Schrödinger on a complete non-compact manifold. It is known since the work of Fischer-Colbrie and Schoen that the finiteness of the negative spectrum of H implies the existence of a function φ solution of Hφ=0 outside a compact set. This has consequences for minimal surfaces and for the finitenes…
Ricci flow singularities on compact Kähler surfaces are of Type I.
problem Understanding finite time singularities of Ricci flow on compact Kähler surfaces.
method Analyzing the Type I property of singularities.
result Non-collapsed finite time singularities are of Type I.
This paper proposes a technique for the unsupervised detection and tracking of arbitrary objects in videos. It is intended to reduce the need for detection and localization methods tailored to specific object types and serve as a general framework applicable to videos with varied objects, backgrounds, and image qualiti…
Study shows Bitcoin security tied to mining rewards and prices.
problem Understanding Bitcoin security's dependency on market outcomes.
method Used ARDL approach with daily blockchain and Bitcoin data from 2014-2019.
result Bitcoin security outcomes linked to Bitcoin price and mining rewards.
Study shows infinite manifold types for every group.
problem Finding manifold types for every finite group.
method Proved existence of infinitely many compact complex hyperbolic 2-manifolds.
result For every finite group, there are infinitely many isomorphism classes of compact complex hyperbolic 2-manifolds with automorphism group isomorphic to the group.
Study complex Monge-Ampère equations on compact Kähler manifolds.
problem Finite energy range of complex Monge-Ampère operator.
method Survey and general answer to Guedj-Zeriahi's question.
result General answer to Guedj-Zeriahi's question about finite energy range.
Proofs show finite subgroups of homeomorphism groups are almost nilpotent.
problem Finite subgroups of homeomorphism groups of compact topological manifolds.
method Finite group theoretic results provide a general strategy for proving Jordan-type theorems.
result Proof of the revised Ghys conjecture about nilpotent normal subgroups.
We construct a connected finite loop space of rank 66 and dimension 1254 whose rational cohomology is not isomorphic as a graded vector space to the rational cohomology of any compact Lie group, hence providing a counterexample to a classical conjecture. Aided by machine calculation we verify that our counterexample is…
No spin structures found in a hyperbolic 4D space.
problem Finding hyperbolic 4-manifolds without spin structures.
method Constructed a non-compact, orientable, hyperbolic 4-manifold.
result Demonstrated existence of a hyperbolic 4D space without spin structures.
Study generalizations of chainability and compactness in metric spaces.
problem Understanding new properties of subsets in metric spaces.
method Exploring and relating new properties of chainability and compactness to existing hypertopologies.
result Relations among Hausdorff, Vietoris, and locally finite hypertopologies established.