Develops rough set classifiers using confusion matrices.
problem Evaluating classifier quality in machine learning.
method Combines rough set theory with confusion matrices.
result Defines indices and classifiers based on rough confusion matrices.
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48 results for “Rough Set”
We introduce a notion of p-rough integrator on any Banach manifolds, for any , which plays the role of weak geometric Holder p-rough paths in the usual Banach space setting. The awaited results on rough differential equations driven by such objects are proved, and a canonical representation is given if the man…
Paper explores rough path theory for frictionless markets, linking NCFL to unbiased rough integrators.
problem Tackles the limits of rough path theory in frictionless markets.
method Investigates the capacity of rough path theory to support No Free Lunch markets.
result Establishes a 'Rough Kreps-Yan' theorem linking NCFL to unbiased rough integrators.
The paper proves signatures of non-geometric rough paths can approximate functionals uniformly.
problem Approximating functionals of non-geometric rough paths.
method Extending rough paths with time and quadratic variation terms, proving uniform approximation.
result Linear functionals of extended signatures uniformly approximate continuous functionals.
Model rough volatility using RDEs with correlated Brownian motion and fractional Brownian motion.
problem Modeling rough volatility with correlated stochastic processes.
method Developed a method to lift Brownian motion and rough paths, applying it to fractional Brownian motion to model rough volatility.
result Calibrated a new rough volatility model to market data.
Estimates roughness of volatility from discrete variance data.
problem Estimating roughness exponent of stochastic volatility from discrete observations of integrated variance.
method Pathwise estimator based on fractional Brownian motion with drift.
result Strong consistency theorems for rough volatility models.
Eigenvalue asymptotics for weighted Laplace equations on rough Riemannian manifolds with boundarymath.DG
Study finds eigenvalue patterns on rough manifolds with measurable metrics.
problem Eigenvalue patterns on rough Riemannian manifolds with measurable metrics.
method Demonstrated a Weyl law for eigenvalues of Laplacian and weighted Laplace equations.
result Eigenvalue asymptotics for weighted Laplace equations on rough Riemannian manifolds.
New method for precise option pricing in stochastic volatility models.
problem Analyzing large classes of stochastic volatility models for robust option pricing.
method Theory of regularity structures and Laplace method on the space of models.
result Precise asymptotics for European options in rough volatility models.
Study rough Riemannian metrics on manifolds, proving their connectedness and completeness.
problem Understanding the space of all locally elliptic and bounded Riemannian metrics on manifolds.
method Introduced an extended metric space and proved its properties.
result Proved the space of rough Riemannian metrics is complete and connected.
Unified approach to stochastic control, filtering, and stopping using rough paths.
problem Addressing gaps in classical problems of stochastic control, filtering, and stopping.
method Combining rough path theory with controlled rough paths to provide a pathwise deterministic framework.
result Established rigorous connection between candidate solutions and Hamilton-Jacobi-Bellman equation.
New methods for volatility modeling using rough paths and signatures.
problem Calibrating implied volatility surfaces in various stochastic models.
method Analytical approximations and signature-based models based on rough path theory.
result Signature-based models achieve comparable accuracy to analytical expansions and can capture more complex dynamics.
Develops geometric integration for rough differential forms.
problem Integrating rough differential forms with low regularity.
method Uses rough path theory to construct geometric integration.
result Constructs geometric integration for rough differential forms.
Efficiently price VIX options using multilevel Monte Carlo in rough Bergomi model.
problem Pricing VIX options in a rough Bergomi model with high computational complexity.
method Combining rectangle discretization, Cholesky sampling, and multilevel Monte Carlo.
result Reduced computational complexity to and asymptotically optimal .
Paper develops a new estimator for rough volatility parameters.
problem Estimating rough volatility parameters from high-frequency data.
method Develops a semiparametric estimator for in rough volatility models.
result The estimator achieves optimal convergence rate in minimax sense.
Market maker optimizes SPX and VIX spread using quadratic rough Heston model.
problem Maximizing profit from SPX and VIX spread while managing inventory risk.
method Uses quadratic rough Heston model to optimize multi-asset market making problem, approximating high-dimensional optimization.
result Asymptotic closed-form solution for optimization problem.
Rough volatility models are very appealing because of their remarkable fit of both historical and implied volatilities. However, due to the non-Markovian and non-semimartingale nature of the volatility process, there is no simple way to simulate efficiently such models, which makes risk management of derivatives an int…
We construct low regularity solutions of the vacuum Einstein constraint equations. In particular, on 3-manifolds we obtain solutions with metrics in $H^s\loc$ with . The theory of maximal asymptotically Euclidean solutions of the constraint equations descends completely the low regularity setting. Moreove…
Framework for training stochastic spiking neural networks with rough signals.
problem Training stochastic spiking neural networks with noisy spike timing and dynamics.
method Rough path theory and signature kernels for gradient computation.
result Pathwise gradients of SSNNs' trajectories and event times exist and satisfy a recursive relation.
On the rate of convergence of estimating the Hurst parameter of rough stochastic volatility modelsq-fin.ST
Paper extends a method to estimate Hurst parameter for rough stochastic volatility models.
problem Estimating Hurst parameter of rough stochastic volatility models from discrete observations.
method Extends a scale-invariant estimator to a general nonlinear function.
result Consistent estimation of Hurst parameter for a wide class of rough stochastic volatility models.
Develops a new model-free approach to portfolio theory using rough paths.
problem Handles more general portfolios without probabilistic assumptions.
method Rough path theory for stochastic portfolio theory (SPT).
result Asymptotic growth rates of various portfolios match.
The paper introduces surface signatures for irregular surfaces and rough surfaces.
problem Characterizing and integrating highly irregular paths and surfaces.
method Introducing surface signatures and proving extension theorems.
result Surface signatures are universal for surface holonomy and rough surfaces.
Comparison results for rough and non-rough Heston models, tighter bounds on moment explosion times.
problem Comparing Heston models with and without roughness.
method Comparison principle for non-linear Volterra integral equations.
result Tighter bounds on moment explosion times for rough Heston models.
Smooth bundles with rough data maintain Hodge kernel isomorphism.
problem Maintaining Hodge kernel isomorphism for smooth bundles with non-smooth geometric data.
method Analyzing nilpotent differential operators and Hodge-Dirac-type operators under perturbations of geometric data.
result Kernels of Hodge-Dirac operators remain isomorphic under uniform perturbations of geometric data.
Study rough volatility models using path-dependent PDEs and fractional Brownian motions.
problem Modeling and analyzing rough volatility in financial markets.
method Showed conditional expectations are unique classical solutions to path-dependent PDEs derived from functional Itô formula. Leverage these to study weak rates of convergence for discretized stochastic integrals.
result Obtained optimal weak error rates for approximating log-stock prices in rough volatility models.
A rough SABR formulaq-fin.MF
Derives a rough SABR formula for short maturities.
problem Modeling volatility smiles under rough volatility.
method Derives an ODE and solves it numerically.
result Develops a very accurate approximation called the rough SABR formula.
Study finds roughness in volatility despite diffusive instantaneous volatility.
problem Determining the roughness of volatility in financial assets.
method Non-parametric method based on normalized -th variation for estimating roughness of sample paths.
result Realized volatility exhibits rough behavior with a significantly smaller Hurst exponent than instantaneous volatility.
Model captures rough volatility and jump clustering in stock vol dynamics.
problem Capturing the joint evolution of S&P 500 and VIX implied vol smiles.
method Rough Hawkes Heston model with affine Volterra dynamics, power kernel, and exponential jump law.
result Model accurately captures S&P 500 and VIX implied vol smiles with low power kernel.
Develops a new method for quantizing rough volatility for volatility derivatives pricing.
problem Pricing volatility derivatives in rough volatility models.
method Functional quantization of rough volatility using offline computable quantizers.
result Pricing VIX Futures in the rough Bergomi model shows competitive results.
Short-time expansion of characteristic functions in a rough volatility setting with applicationsq-fin.ST
We derive a higher-order expansion for rough volatility models.
problem Characterizing and estimating rough volatility models.
method Higher-order asymptotic expansion of characteristic functions.
result Distinct roles of rough and jump dynamics in volatility.
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.
Paper uses machine learning to estimate IRI from pavement distress types, densities, and severities.
problem Costly IRI measurements exclude many road classes; estimating IRI from distress data is needed.
method Data from in-service pavements; machine learning methods used to predict IRI.
result Machine learning can reliably estimate IRI based on distress types, densities, and severities.
Measures of implied volatility roughness corrected for bias.
problem Bias in measuring implied volatility roughness.
method Examined implied volatility of short-term options and VIX index, corrected for bias.
result Corrected measures indicate appropriate proxies for underlying volatility.
This study simplifies rough Heston model's conditional density equation.
problem Analyzing rough volatility in financial models.
method Pathwise transformation and Fokker-Planck formulation of conditional density equation.
result Transformed equation yields deterministic PDE with path-dependent coefficients.
We introduce novel equations, in the spirit of rough path theory, that parametrize level sets of intrinsically regular maps on the Heisenberg group with values in . These equations can be seen as a sub-Riemannian counterpart to classical ODEs arising from the implicit function theorem. We show that they e…
Estimates roughness of stochastic processes without assuming specific models.
problem Estimating roughness of stochastic processes without assuming specific models.
method Using Faber-Schauder coefficients and martingales, we provide a method to estimate the roughness exponent of stochastic processes.
result The roughness exponent can be estimated without assuming specific models, providing a strong consistency result for the Gladyshev estimators.
Affine Rough Modelsq-fin.MF
Explains affine rough models and their transform formulas.
problem Rough volatility models in financial markets.
method Explains affine structure and transforms formulas.
result Shows exponential-affine transform formulas for rough models.
Study finds rough volatility models underperform in SPX option pricing.
problem Inconsistency of rough volatility models with SPX option prices.
method Empirical study using SPX options data, comparing rough and Markovian models.
result Rough volatility models with are inconsistent with SPX smiles, especially at short maturities.
Extreme learning machine (ELM) is a new single hidden layer feedback neural network. The weights of the input layer and the biases of neurons in hidden layer are randomly generated, the weights of the output layer can be analytically determined. ELM has been achieved good results for a large number of classification ta…
Fuzzy Rough Set selects key features for phishing detection.
problem Efficient feature selection for phishing detection.
method Fuzzy Rough Set (FRS) theory for feature selection.
result Maximum F-measure of 95% using Random Forest.
New gene selection method improves tumor classification accuracy.
problem Efficiently selecting relevant genes from high-dimensional tumor gene expression data.
method Fuzzy-Rough Set Theory for feature dependency analysis.
result The proposed method outperforms state-of-the-art techniques in tumor classification.
New methods price American options in rough volatility models.
problem Pricing American options under rough volatility.
method Integrating deep-signature and signature-kernel learning into optimal stopping problem solutions.
result Performance comparison in rough Heston and rough Bergomi models.
Study approximates weak error for specific stochastic models with rough and Gaussian mean-reverting volatility.
problem Approximating weak error for specific stochastic models with rough and Gaussian mean-reverting volatility.
method Used Euler type scheme with integrated kernels to study weak convergence rate.
result Obtained weak convergence rate of for discretised rough Ornstein-Uhlenbeck process and stochastic rough volatility model.
Rough geometric integrationmath.DG
Integrates rough geometric forms on manifolds.
problem Integrating rough forms on complex manifolds.
method Combines Whitney's geometric integration and sewing approaches.
result Introduced distributional k-forms for integration.
Study approximates rough stochastic volatility models using diffusion processes.
problem High computational cost in simulating rough stochastic volatility models.
method Approximates stochastic Volterra equations with an N-dimensional diffusion process.
result Approximations converge strongly with superpolynomial rate in N.
Volatility has to be roughq-fin.MF
Volatility models must be rough to match market skew.
problem Inconsistent non-rough volatility models with power law volatility skew.
method Asymptotic expansion and continuous price dynamics analysis.
result Volatility must be rough to align with market skew.
Gamma Hedging and Rough Pathsq-fin.MF
Study of gamma-hedging using rough paths for European and exotic options.
problem Applying rough paths to gamma-hedging strategies for derivatives.
method Rough-path theory applied to discrete-time gamma-hedging strategy.
result Sure replication of European and exotic derivatives under regular pricing signals.
Paper tackles rough volatility estimation from high-frequency data.
problem Estimating historical volatility from high-frequency asset price data.
method Uses fractional Brownian motion representation and particle methods for filtering and parameter estimation.
result Demonstrates efficient estimation of rough volatility using standard techniques.
The paper analyzes robustness and sensitivity of rough Volterra stochastic volatility models.
problem Analyzing the robustness and sensitivity of stochastic volatility models.
method Statistical tests and empirical analysis on Apple Inc. equity options.
result Comparison of different models' robustness and sensitivity to option data structure.