The paper analyzes skewness and kurtosis measures for skew-elliptical distributions.
problem Examining skewness and kurtosis measures for skew-elliptical distributions.
method Deriving exact expressions for skewness and kurtosis measures for skew-elliptical distributions, constructing test statistics, and comparing measures through simulations and real data analysis.
result Exact expressions and test statistics for skewness and kurtosis measures for various skew-elliptical distributions.
Optimizes option portfolios for skewed-t returns using VaR and variance measures.
problem Optimizing portfolios for skewed-t returns with heavy tails and skewness.
method Uses variance and VaR measures, departing from normal returns, and provides explicit portfolio weights.
result Optimal portfolio weights differ significantly from variance optimal weights due to skewness.
The paper calculates moments and conditional risks for skewed elliptical distributions.
problem Estimating moments and tail conditional risks for skewed elliptical distributions.
method Derives explicit expressions for multivariate doubly truncated moments and conditional risks for generalized skew-elliptical distributions.
result Explicit formulas for multivariate doubly truncated moments and conditional risks are derived for various skewed elliptical distributions.
Study refracted skew Brownian motion, find densities and asymptotics.
problem Modeling and analyzing refracted skew Brownian motion.
method Perturbation approach to find potential densities, transition density, and asymptotic behaviors.
result Expressions and asymptotic behaviors of refracted skew Brownian motion.
New divergence measures improve KL approximation.
problem Improving KL divergence approximation without AC condition.
method Introduced α-geodesical skew divergence. result Properties of α-geodesical skew divergence studied. The left tail of the implied volatility skew, coming from quotes on out-of-the-money put options, can be thought to reflect the market's assessment of the risk of a huge drop in stock prices. We analyze how this market information can be integrated into the theoretical framework of convex monetary measures of risk. In …
Under a generalized skew normal distribution we consider the problem of European option pricing. Existence of the martingale measure is proved. An explicit expression for a given European option price is presented in terms of the cumulative distribution function of the univariate skew normal and the bivariate standard …
We derive measure change formulae required to price midcurve swaptions in the forward swap annuity measure with stochastic annuities' ratios. We construct the corresponding linear and exponential terminal swap rate pricing models and show how they capture the midcurve swaption correlation skew.
A new method for efficiently computing derivatives of skew-symmetric matrix exponentials.
problem Efficient computation of derivatives for skew-symmetric matrices.
method Characterization of invertibility, construction of nearby logarithm, and efficient implementation.
result Explicit formulae for differentiation and its inverse of skew-symmetric matrix exponentials.
This work accelerates constrained sampling using large deviation principles.
problem Sampling constrained probability distributions efficiently.
method Large deviation principles applied to skew-reflected non-reversible Langevin dynamics.
result The skew-symmetric matrix accelerates convergence and reduces asymptotic variance.
We reformulate Lehmer's question from 1933 and a question due to Schinzel and Zassenhaus from 1965 in terms of a comparison of the Mahler measures and the houses, respectively, of monic integer reciprocal and skew-reciprocal polynomials of the same degree. This entails that understanding the difference between orientat…
In this paper, we present a method for constructing a (static) portfolio of co-maturing European options whose price sign is determined by the skewness level of the associated implied volatility. This property holds regardless of the validity of a specific model - i.e. the method is robust. The strategy is given explic…
New inflation model captures correlations and skew in interest rates.
problem Modeling inflation with market correlations and skew.
method Multi-factor volatility structure with parametric correlation calibration, leveraging single-factor Gaussian model.
result Captures market volatility skew with a single process, simplifying model calibration.
Conditional Autoregressive Value-at-Risk and Conditional Autoregressive Expectile have become two popular approaches for direct measurement of market risk. Since their introduction several improvements both in the Bayesian and in the classical framework have been proposed to better account for asymmetry and local non-l…
Local logarithmic export distributions show non-zero skewness that changes with exporter and destination characteristics.
problem Identifying the skewness in local logarithmic export distributions and its relationship with exporter and destination characteristics.
method Analyzing directed links weighted by the logarithm of export values, studying the skewness of local exports, and formulating quantitative relations.
result Non-zero skewness in local logarithmic export distributions changes with exporter and destination characteristics.
Mostow rigidity proven for special geometric manifolds.
problem Proving rigidity for specific geometric structures.
method Analyzing foliated bundles over closed hyperbolic manifolds with invariant measures.
result Mostow rigidity theorem extended to skew solenoidal manifolds.
ABROCA assesses algorithmic bias, revealing skewed distributions that inflate results.
problem Detecting nuanced performance differences in classifier fairness.
method Study of ABROCA metric's statistical properties under various conditions.
result ABROCA distributions are skewed, inflating results by chance in imbalanced classes.
We revisit the problem of pricing options with historical volatility estimators. We do this in the context of a generalized GARCH model with multiple time scales and asymmetry. It is argued that the reason for the observed volatility risk premium is tail risk aversion. We parametrize such risk aversion in terms of thre…
The paper defines MTCov for skewed elliptical distributions.
problem No specific problem stated, but dealing with skewed elliptical distributions.
method Defined MTCov for generalized skew-elliptical distributions and compared with skewed and non-skewed normal distributions.
result Special formula for MTCov of generalized skew-elliptical distributions.
The ADO-Heston model approximates market implied skew in vanilla options.
problem Reproduce market implied skew in vanilla options using a Markovian approximation.
method Derived characteristic function under risk-neutral and real measures, chose market price of risk, found closed form for log-price CF and implied skew.
result The ADO-Heston model can approximate the vanilla implied skew at small T but not exactly as rough volatility models. Novel criterion identifies heteroscedastic noise in causal discovery.
problem Heteroscedastic noise violates equal-variance assumption in causal discovery.
method Skewness-based criterion for identifying HSNMs.
result Skewness-based criterion distinguishes causal from anticausal directions.
This study assesses the impact of non-IID data in federated learning, revealing significant performance drops.
problem The impact of non-IID data on federated learning model performance.
method Empirical analysis using Hellinger Distance to measure distribution differences, benchmarking four strategies for handling non-IID data.
result Significant performance drops occur at specific HD thresholds, especially for extreme non-IIDness.
Paper proposes MUCS for more reliable TDA in diffusion models.
problem Current TDA approaches lack reliability and robustness.
method Mirrored unlearning and noise-consistent skew (MUCS).
result MUCS outperforms existing methods on three datasets.
Improved portfolio optimization using VaR and CVaR with NMVM models.
problem Optimizing portfolios with VaR and CVaR under NMVM distributions.
method Transformed mean-CVaR-skewness problems into quadratic optimization with closed-form solutions for NMVM models.
result Approximate closed-form expressions for VaR and CVaR of NMVM portfolios.
Proposes a method to identify elements in a skewness matrix for multivariate skew-elliptical distributions.
problem Label switching issue in Bayesian estimation of skewness matrix.
method Imposes a positive lower-triangular constraint and uses Bayesian sparse estimation with horseshoe prior.
result Successfully estimates the true structure of skewness dependency.
Enhances knot counting invariant using skew braces.
problem Counting invariant for virtual knots and links.
method Introduces new invariants using skew brace structures.
result New invariants not determined by the counting invariant.
Study the geometry and dynamics of skew evolutes and involutes, related to bicycle kinematics.
problem Understanding the geometry and dynamics of skew evolutes and involutes.
method Investigate the skew evolute and involute maps, comparing them to bicycle kinematics.
result The skew evolute and involute maps have properties analogous to bicycle kinematics.
Study on simplicity of Lie skew braces, proving new results for compact cases.
problem Simplicity of Lie skew braces, focusing on compact connected cases.
method Reviewing correspondence, investigating ideals and rigidity, proving main result for compact Lie skew braces.
result Compact connected simple Lie skew braces are either trivial or have simple underlying Lie groups.
The paper examines smoothness in graded skew Clifford algebras.
problem Smoothness of graded skew Clifford algebras.
method Investigation of differential smoothness.
result Results on the differential smoothness of graded skew Clifford algebras.
Proposes a new method for big portfolio selection using graph-based conditional moments.
problem Challenges in selecting portfolios for thousands of stocks.
method Graph-based Conditional Moments (GRACE) method: learns quantiles, means, variances, skewness, and kurtosis of stock returns.
result Shows superior performance compared to competitors, especially in measures of conditional variance, skewness, and kurtosis.
A skew loop is a closed curve without parallel tangent lines. We prove: The only complete surfaces in euclidean 3-space with a point of positive curvature and no skew loops are the quadrics. In particular, ellipsoids are the only closed surfaces without skew loops. We also prove results about skew loops on cylinders an…
Simple method solves Quanto Skew problem.
problem Quanto Skew problem in Equities and FX.
method Analytical method that accommodates Equity and FX volatility skew.
result Highly efficient and fast performance.
Skewness dispersion predicts future stock market returns, especially in months with monetary policy announcements.
problem Predicting future stock market returns using skewness dispersion.
method Cross-sectional analysis of firm-level realized skewness and stock market returns.
result Skewness dispersion is a significant predictor of future stock market returns, robust to various estimation methods.
New topological biquandles created using skew braces.
problem Creating nontrivial topological biquandles.
method Using the concept of skew braces.
result Constructs nontrivial examples of topological biquandles.
Examines differential smoothness in a specific skew PBW extension family.
problem Differential smoothness in skew PBW extensions.
method Investigates a specific family of skew PBW extensions.
result Results on differential smoothness of the family.
The asymptotic behavior of open plane sections of triply periodic surfaces is dictated, for an open dense set of plane directions, by an integer second homology class of the three-torus. The dependence of this homology class on the direction can have a rather rich structure, leading in special cases to a fractal. In th…
New condition ensures submanifolds are skew in small areas.
problem Ensuring submanifolds are skew in Euclidean space.
method Introduces a third-order differential condition.
result Constructs improved totally skew embeddings for Rn. A skew brane is an immersed codimension 2 submanifold in affine space, free from pairs of parallel tangent spaces. Using Morse theory, we prove that a skew brane cannot lie on a quadratic hypersurface. We also prove that there are no skew loops on embedded ruled developable discs in 3-space. The paper extends recent wo…
This paper classifies 4D spin manifolds with skew Killing spinors.
problem Classifying 4D Riemannian spin manifolds with skew Killing spinors.
method Analyzing skew Killing spinors with skew-symmetric endomorphisms A, considering both degenerate and non-degenerate cases.
result In the degenerate case, the manifold is locally isometric to R x N with N having a skew Killing spinor.
Complete classification of quaternionic skew-Hermitian symmetric spaces found.
problem Classifying quaternionic skew-Hermitian symmetric spaces.
method Proving the existence of a torsion-free mSO∗(2n)mSp(1)-structure and showing that any homogeneous space is symmetric. result A complete classification of quaternionic skew-Hermitian symmetric spaces for arbitrary n>1. Paper defines new risk measures for elliptical distributions.
problem Risk measurement for elliptical distributions.
method DTM, DTS, DTK definitions and formula derivation for specific distributions.
result Explicit formulas for DTE, DTV, DTS, and DTK for various distributions.
Following recent work by Ghomi, Solomon and Tabachnikov, we study geometry and topology of skew branes. A skew brane is a codimension 2 submanifold in affine space such that the tangent spaces at any pair of distinct points are not parallel. We prove that if an oriented closed manifold has a non-zero Euler characterist…
New RESK distributions improve robust clustering of skewed data.
problem Robustly clustering non-symmetric, heavy-tailed data clusters.
method Proposes RESK distributions and an EM algorithm with robust skew-Huber M-estimator.
result Numerical experiments confirm the effectiveness of the proposed methods.
The paper examines differential smoothness in skew PBW extensions over polynomial rings.
problem Differential smoothness in skew PBW extensions over polynomial rings.
method Investigation of skew PBW extensions over commutative polynomial rings.
result Results on differential smoothness for skew PBW extensions over polynomial rings.
A parsimonious model reduces over-parameterization in skewed matrix variate mixtures.
problem Over-parameterization in skewed matrix variate mixtures.
method Parsimonious family of 256 models using bilinear factor analyzers constrained over clusters, with AECM algorithm for estimation.
result Extensive simulations and real-world datasets (MNIST, Olivetti faces) demonstrate the method's effectiveness.
Study various submanifolds in quaternionic skew-Hermitian spaces.
problem Characterize submanifolds in almost quaternionic skew-Hermitian manifolds.
method Construct explicit examples of submanifolds in semisimple quaternionic skew-Hermitian symmetric spaces.
result Explicit examples of submanifolds for each type considered.
Study investigates how preprocessing, feature selection, and model selection affect performance on imbalanced genetic data.
problem Challenges in using machine learning on imbalanced genetic datasets.
method Comparative analysis of data preprocessing, feature selection techniques, and machine learning models on imbalanced genetic data.
result Class-imbalanced target variables and skewed predictors have little to no impact on classification performance.
The paper improves asset allocation using a skew-normal distribution in the Black-Litterman model.
problem Improving asset allocation under skewed return distributions.
method Using the Black-Litterman model with hidden truncation skew-normal distribution and Simaan's three-moment risk model.
result Optimal portfolios have less risk and higher skewness compared to classical BL model.