The paper studies nilpotent structures in oriented neutral vector bundles and neutral hyperKähler structures.
problem Nilpotent structures in oriented neutral vector bundles and their relation to neutral hyperKähler structures.
method Defined H-nilpotent structures for Lie subgroups of SO(2n,2n) related to neutral hyperKähler structures. result Existence of complex and paracomplex structures forming neutral hyperKähler structures if and only if there exists an H-nilpotent structure. Novel methods transform correlated neutral vectors into independent variables.
problem Decorrelating correlated neutral vector variables that are not multivariate Gaussian distributed.
method Serial and parallel nonlinear transformations to achieve mutual independence.
result Highly negatively correlated neutral vectors can be transformed into mutually independent scalar variables.
Enhances EEG signal classification using non-Gaussian neutral vectors.
problem Challenges in classifying EEG signals for brain-computer interfaces.
method Transformed mDWT coefficients into neutral vectors, applied feature selection.
result Feature selection improves classification accuracy.
The study classifies meridian surfaces with specific curvature properties in a special 4D space.
problem Characterizing surfaces with parallel mean or normalized mean curvature vectors.
method Classification of meridian surfaces based on curvature properties.
result Existence of surfaces with parallel normalized mean curvature but not mean curvature.
Study on surfaces in pseudo-Euclidean space with neutral metric.
problem Characterizing surfaces in pseudo-Euclidean 4-space with neutral metrics.
method Defined and studied Lorentz general rotational surfaces with specific properties.
result Complete classification of various types of general rotational surfaces.
The study classifies special Lorentz surfaces in a 4-space with neutral metric.
problem Classifying meridian surfaces in a pseudo-Euclidean 4-space.
method Constructing and classifying meridian surfaces with specific properties.
result There exist meridian surfaces with parallel normalized mean curvature vector field but not parallel mean curvature vector.
Currently, machine learning plays an important role in the lives and individual activities of numerous people. Accordingly, it has become necessary to design machine learning algorithms to ensure that discrimination, biased views, or unfair treatment do not result from decision making or predictions made via machine le…
Study null conformal Killing vector fields on complex surfaces.
problem Characterize pseudo-Hermitian surfaces with null vector fields.
method Analyze topological types and use vector fields to define para-hyperhermitian structures.
result Classify compact four-manifolds with orthogonal null Killing vector fields.
Paper proposes GN-GloVe to learn gender-neutral word embeddings.
problem Inherit strong gender stereotypes in embeddings trained on human-generated corpora.
method Proposes a novel training procedure to isolate gender information in word vectors.
result GN-GloVe successfully isolates gender information without sacrificing functionality.
Study on surfaces in neutral space forms with zero mean curvature.
problem Characterizing surfaces with zero mean curvature in neutral space forms.
method Analyzing curvature and normal connection properties of time-like conformal immersions.
result Conditions for surfaces with zero mean curvature in neutral space forms.
The theory of harmonic vector fields on Riemannian manifolds is generalised to pseudo-Riemannian manifolds. Harmonic conformal gradient fields on pseudo-Euclidean hyperquadrics are classified up to congruence, as are harmonic Killing fields on pseudo-Riemannian quadrics. A para-Kaehler twisted anti-isometry is used to …
While the Lorenzian and Riemanian metrics for which all polynomial scalar curvature invariants vanish (the VSI property) are well-studied, less is known about the four-dimensional neutral signature metrics with the VSI property. Recently it was shown that the neutral signature metrics belong to two distinct subclasses:…
Model predicts political ideology using context vectors to mitigate bias and scarcity.
problem Scarcity and selection bias in political ideology prediction.
method Proposes a statistical model decomposing embeddings into context and position vectors, training an end-to-end model for deployment.
result Model can predict ideological labels even with minimal biased data, outperforming state-of-the-art methods.
Study on holomorphic discs in bundles over compact surfaces, proving Fredholm regularity under certain conditions.
problem Analyzing holomorphic discs with boundary on surfaces in vector bundles over compact manifolds.
method Proves Fredholm regularity for sections with a single complex point under specific conditions.
result Holomorphic discs are Fredholm regular under certain conditions, including neutral Kähler and symplectic actions.
Synthesizes faces from facial features, invariant to pose and expression.
problem Creating realistic face images from facial features.
method Learning facial landmarks and textures from facial-recognition features, training on frontal, neutral-expression images.
result Generated images are invariant to lighting, pose, and expression.
Characterizes neutral deformation modes of minimal surfaces.
problem Understanding the energy content of deformation modes of minimal surfaces.
method Analyzes the energy content of stretching, drilling, and bending modes of minimal surfaces.
result All isometries of a minimal surface are globally neutral and give rise to soft elasticity.
A Lorentz surface in the four-dimensional pseudo-Euclidean space with neutral metric is called quasi-minimal if its mean curvature vector is lightlike at each point. In the present paper we obtain the complete classification of quasi-minimal Lorentz surfaces with pointwise 1-type Gauss map.
Paper introduces benchmark-neutral pricing for long-term contracts.
problem High prices of long-term contracts under risk-neutral pricing.
method Uses growth optimal portfolio as numeraire and new pricing measure.
result Identifies minimal possible prices for contingent claims.
Study finds all 4D neutral manifolds.
problem Classifying neutral manifolds in four dimensions.
method Examined homogeneous semi-symmetric neutral manifolds.
result Identified all four-dimensional neutral manifolds.
The purpose of this article is to review some recent results on the geometry of neutral signature metrics in dimension four and their twistor spaces. The following topics are considered: Neutral Kähler and hyperkähler surfaces, Walker metrics, Neutral anti-self-dual 4-manifolds and projective structures, Twistor spaces…
In the four-dimensional pseudo-Euclidean space with neutral metric there are three types of rotational surfaces with two-dimensional axis - rotational surfaces of elliptic, hyperbolic or parabolic type. A surface whose mean curvature vector field is lightlike is said to be quasi-minimal. In this paper we classify all q…
The paper explores neutral 4-manifolds with null boundaries using causal topology.
problem Neutral 4-manifolds with null boundaries and their topological properties.
method Neutral causal topology, foliation of null hypersurfaces, and geometric constructions.
result Neutral 4-manifolds with null boundaries and their topological properties.
Bayesian MS-VAR process improves option pricing models.
problem Improving option pricing models for better accuracy.
method Bayesian Markov-Switching Vector Autoregressive (MS-BVAR) process with risk-neutral valuation.
result Derived pricing formulas for various options.
Optimizes risk-neutral probabilities for derivative pricing.
problem Deriving bounds on derivative values under multiple risk-neutral scenarios.
method Convex optimization over the set of risk-neutral probability distributions.
result Tractable finite-dimensional optimization problems for pricing.
Using twistor methods, we explicitly construct all local forms of four--dimensional real analytic neutral signature anti--self--dual conformal structures (M,[g]) with a null conformal Killing vector. We show that M is foliated by anti-self-dual null surfaces, and the two-dimensional leaf space inherits a natural pr…
Paper introduces R-conditioning for risk-averse valuation in financial markets.
problem Risk-averse valuation in incomplete financial markets.
method Introduces R-conditioning as a new operator between conditional expectation and sublinear expectation.
result R-conditioning can approximate sublinear expectations and is used to compute risk-averse values.
The paper shows how to calculate risk-neutral default probabilities from bid and ask CDS quotes.
problem Calculating risk-neutral default probabilities from market quotes.
method Using conic finance framework and Poisson process to formulate and solve the calibration problem.
result A unique solution for risk-neutral default probabilities and implied liquidity.
Simulates risk-neutral markets using neural spline flows.
problem Creating realistic risk-neutral market simulations.
method Developed a low-dimensional martingale representation and used neural spline flows for sampling.
result The calibrated simulator is closest to historical data with respect to Kullback-Leibler divergence.
We study the isometry groups and Killing vector fields of a family of pseudo-Riemannian metrics on Euclidean space which have neutral signature (3+2p,3+2p). All are p+2 curvature homogeneous, all have vanishing Weyl scalar invariants, all are geodesically complete, and all are 0-curvature modeled on an indecomposible s…
Generative model uses DDPMs for risk-neutral derivative pricing.
problem Derivative pricing using arbitrage-free models.
method Developed a framework using DDPMs to generate risk-neutral asset price dynamics.
result Empirically validated the method for both European and path-dependent derivatives.
We review the subject of four dimensional anti-self-dual conformal structures with signature (+ + - -). Both local and global questions are discussed. Most of the material is well known in the literature and we present it in a way which underlines the connection with integrable systems. Some of the results - e.g. the L…
The paper characterizes surfaces in 4D space forms with flat normal connection.
problem Characterizing surfaces in 4D space forms with specific geometric properties.
method Analyzing linearly dependent conditions and using properties of sectional curvature.
result Characterizations of space-like and time-like surfaces with flat normal connection.
The aim of this paper is to give examples of compact neutral 4-manifolds (M,g) whose Ricci tensor ρ satisfies the relation ∇Xρ(X,X)=31Xτg(X,X). We present also a family of new Einstein bi-Hermitian neutral metrics on ruled surfaces of genus g>1.
The paper shows that benchmark-neutral pricing minimizes option prices.
problem Pricing extreme-maturity European put options on diversified indices.
method Benchmark-neutral pricing applied to a drifted time-transformed squared Bessel process.
result Benchmark-neutral price is the minimal possible price, risk-neutral price is more expensive.
Project estimates risk-neutral dependence from option prices.
problem Extracting risk-neutral dependence from option prices.
method Projection estimator using portfolios of observed options.
result Estimates risk-neutral dependence in incomplete markets.
A new beta model reduces bias in market neutral strategies.
problem Bias in beta estimation for market neutral strategies.
method Derive a metric of correlation with leverage effect to identify market beta and volatility changes.
result Empirical test confirms the reactive beta model's ability to reduce bias.
Paper studies pricing and hedging of nonreplicable insurance contracts using benchmark-neutral approach.
problem Pricing and hedging of long-term insurance contracts like variable annuities.
method Benchmark-neutral pricing framework using stock growth optimal portfolio as numéraire.
result Prices can be significantly lower than risk-neutral ones, offering attractive long-term risk-management.
Minimal surfaces can be transformed into others with unchanged bending content.
problem Understanding the deformation properties of minimal surfaces.
method Refined polar decomposition theorem to identify bending-neutral deformations.
result Every minimal surface can be transformed into another by a bending-neutral deformation.
Extends wealth tax neutrality framework to stochastic volatility and non-homothetic preferences.
problem Ensuring wealth taxes are neutral under various economic conditions.
method Extended Frøseth's neutrality framework to stochastic volatility and non-homothetic preferences, identified four channels of non-neutrality, and applied the framework to global minimum wealth taxes.
result Non-uniform assessment, general equilibrium effects, progressive thresholds, and endogenous labour supply can cause non-neutrality under CRRA preferences.
Efficient RL in partially observable risk-sensitive environments with hindsight observations.
problem Risk-sensitive reinforcement learning in partially observable environments.
method Integrates hindsight observations into POMDP framework, develops novel RL algorithm.
result Achieves polynomial regret with provable efficiency, outperforming existing methods.
We reformulate wealth taxation using Fokker-Planck equations to ensure tax neutrality.
problem Ensuring tax neutrality in wealth taxation frameworks.
method Reformulating the neutral wealth tax framework using stochastic dynamics and statistical physics, specifically Fokker-Planck equations.
result The framework clarifies when wealth taxation is a benign rescaling of dynamics and when it introduces new physics.
Generative model prices options and extracts risk-neutral densities.
problem Price options and extract risk-neutral densities from market data.
method Model log-returns as a generative model, using neural nets for location, scale, and higher-order moments, with stringent conditions to avoid arbitrage.
result The model efficiently generates samples to price options and accommodates diverse risk-neutral densities.
Market-neutral pairs-trading strategies are justified by optimal control theory.
problem Investment strategies in cointegrated stocks with CRRA utility.
method Extended optimal control problem with verification result.
result Sharp well-posedness condition for market-neutral pairs-trading.
AlphaZeroBeta uses deep reinforcement learning for market-neutral portfolios, outperforming traditional methods.
problem Traditional portfolio management methods often fail during market regime shifts or when assumptions break down.
method Combines a composite reward function and CNN-GRU policy trained end-to-end via Recurrent PPO.
result Achieves higher Sharpe ratios than baselines while maintaining near-zero benchmark correlations.
Study minimal surfaces in product spaces with neutral metrics.
problem Characterize minimal surfaces in product spaces with neutral metrics.
method Compute totally geodesic surfaces and relate to Gordon equations; classify compact minimal surfaces.
result Provide a topological classification of compact minimal surfaces.
Study finds cryptocurrency market diversity patterns inconsistent with neutral models.
problem Cryptocurrency market diversity patterns not consistent with neutral models.
method Analysis borrowing methods from ecology, focusing on diversity patterns and community structure.
result Cryptocurrency market diversity patterns not consistent with neutral models, suggesting strong interactions between species.
Deep Hedging learns risk-neutral vol dynamics for option pricing.
problem Statistical arbitrage in market dynamics without transaction costs.
method Numerical approach to train market simulator and find risk-neutral density.
result Risk-neutral model for stochastic implied volatility can be used for pricing or Deep Hedging.
Examines GARCH intensity model for risk-neutral option pricing.
problem Volatility clustering, leverage effect, and conditional asymmetry in financial returns.
method Risk-neutral option pricing method under GARCH intensity model.
result Flexibility in volatility changes according to probability measure.