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.
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.
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.
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.
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.
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.
Foundation for robust finance using rough path theory.
problem Mathematical models of financial markets under Knightian uncertainty.
method Introducing Property (RIE) for càdlàg paths, proving existence of rough integrals, verifying admissibility of trading strategies.
result Existence and stability of rough path integrals for non-gradient integrands.
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.
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 s>23. The theory of maximal asymptotically Euclidean solutions of the constraint equations descends completely the low regularity setting. Moreove…
We present a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard to short-time and small noise formulae for option prices. Our main tool is the theory of regularity structures, which we use in the form of [Bayer et al; A regularity structure for rough vola…
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.
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.
Study short-time existence of Ricci-DeTurck flow from rough metrics with Morrey-type integrability.
problem Short-time existence of Ricci-DeTurck flow from rough metrics with specific integrability condition.
method Rough existence theory, preservation and improvement of scalar curvature bounds.
result Preservation and improvement of distributional scalar curvature lower bounds under certain conditions.
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.
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.
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 R2. These equations can be seen as a sub-Riemannian counterpart to classical ODEs arising from the implicit function theorem. We show that they e…
A new model adapts Hurst parameter in real-time for volatility forecasting.
problem Capturing volatility dynamics and clustering in financial markets.
method Rough Bergomi model with EWMA-driven time-dependent Hurst parameter.
result Empirical validation shows superior performance in diverse asset classes.
Novel approach to financial derivatives pricing using rough path theory.
problem No-arbitrage conditions in financial markets necessitating precise integration methods.
method Developed a polynomial-based approximation class for rough path functionals, extending to non-geometric rough paths.
result Motivated a hypothesis for payoff functionals in financial markets, facilitating analysis.
Study Ricci-Deturck flow from rough metrics, proving short-time existence.
problem Short-time existence of Ricci-Deturck flow from rough metrics.
method Ricci-Deturck flow, bi-Lipschitz metrics, small gradient concentration.
result Proved short-time existence of Ricci-Deturck flow.
Researchers develop optimal methods to estimate rough volatility parameters.
problem Statistical inference for rough volatility models with fractional Brownian motion.
method Established minimax lower bounds and designed wavelet-based procedures.
result Optimal speed of convergence n−1/(4H+2) for estimating H. We will show that for a polynomially contractible manifold of bounded geometry and of polynomial volume growth every coarse and rough cohomology class pairs continuously with the K-theory of the uniform Roe algebra. As an application we will discuss non-vanishing of rough index classes of Dirac operators over such mani…
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.
Develops pathwise analysis for log-optimal portfolios using rough paths theory.
problem Analyzing stability and approximation of log-optimal portfolios.
method Pathwise approach based on càdlàg rough paths theory.
result Establishes pathwise stability and error estimates for log-optimal portfolios.
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.
A new paradigm recently emerged in financial modelling: rough (stochastic) volatility, first observed by Gatheral et al. in high-frequency data, subsequently derived within market microstructure models, also turned out to capture parsimoniously key stylized facts of the entire implied volatility surface, including extr…
We introduce a notion of p-rough integrator on any Banach manifolds, for any p≥1, 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…
Study large deviations for hypoelliptic diffusion on sub-Riemannian manifolds.
problem Large deviations for hypoelliptic diffusion measures on sub-Riemannian manifolds.
method Rough path theory and manifold-valued Malliavin calculus.
result Proved a large deviation principle for pinned hypoelliptic diffusion measures.
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.
Adapts EGOP to multi-class setting and proposes a simple rough estimator.
problem Recovering relevant directions for multi-class regression.
method Adapt EGOP to multi-class setting, propose a simple rough estimator.
result Simple rough estimator of EJOP remains statistically consistent.
New study finds actual volatility is rougher than previously thought.
problem Determining if volatility is rough based on log realized volatility data.
method Developed a quasi-likelihood estimator for fractional stochastic volatility model.
result Volatility is indeed rougher than previously estimated.
New method for pricing European options in rough LSV models.
problem Pricing European options in non-Markovian local stochastic volatility models.
method Conditional LSV dynamics, rough path theory, rough partial differential equations (RPDEs).
result Established a PDE pricing method for non-Markovian models.
Paper proposes a new classifier for gender detection in mobile telematics.
problem Detecting gender through mobile telematics data.
method Choquet fuzzy integral vertical bagging classifier combining random forest and rough set theory.
result Choquet fuzzy integral vertical bagging classifier outperforms other classifiers.
Reviews six finance topics, including 'radical complexity'.
problem None explicitly stated, focuses on research directions.
method Informal review and discussion of open questions.
result No specific key result mentioned, focuses on research directions.
Improved approximations for rough Heston model reduce errors.
problem Lack of Markov and semimartingale properties in rough Heston model.
method Markovian approximations with weak error analysis.
result Super-polynomial convergence of new approximations.
We present two different approaches to stochastic integration in frictionless model free financial mathematics. The first one is in the spirit of Itô's integral and based on a certain topology which is induced by the outer measure corresponding to the minimal superhedging price. The second one is based on the controlle…
We bring the theory of rough paths to the study of non-parametric statistics on streamed data. We discuss the problem of regression where the input variable is a stream of information, and the dependent response is also (potentially) a stream. A certain graded feature set of a stream, known in the rough path literature…
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.
Signature Isolation Forest removes constraints from FIF by using rough path theory's signature transform.
problem Challenges in FIF's linear inner product and dictionary choices leading to unreliable results.
method Introduces Signature Isolation Forest using rough path theory's signature transform to remove linearity constraints.
result Demonstrates relevance of methods through numerical experiments and real-world applications.
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.
Our topological setting is a smooth compact manifold of dimension two or higher with smooth boundary. Although this underlying topological structure is smooth, the Riemannian metric tensor is only assumed to be bounded and measurable. This is known as a rough Riemannian manifold. For a large class of boundary condition…
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 O(ε−2log2(ε)) and asymptotically optimal O(ε−2). 2DSig-Detect detects adversarial perturbations in images.
problem Adversarial attacks degrade image model performance.
method 2D-signature embedded semi-supervised framework using rough path theory.
result 2DSig-Detect outperforms other methods in detecting adversarial perturbations.
Paper develops a new estimator for rough volatility parameters.
problem Estimating rough volatility parameters from high-frequency data.
method Develops a semiparametric estimator for H in rough volatility models. result The estimator achieves optimal convergence rate in minimax sense.
Unified RMOT framework for non-modelable risk factors reduces audit bounds.
problem Infinite audit bounds for exotic derivatives pricing with sparse market data.
method Rough Martingale Optimal Transport (RMOT) with rough volatility regularization.
result Finite, explicit, and asymptotically tight extrapolation bounds for non-modelable risk factors.
Estimates roughness of financial volatility paths using horizontal visibility graphs.
problem Estimating roughness in financial volatility models.
method Introduces L+(t) for first-passage horizons, treating uncensored observations as first-passage times.
result Estimates roughness through a single tail exponent θ, separating rough Bergomi volatility from classical models.
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…
Study non-Gaussian measures' concentration properties in metric spaces.
problem Concentration properties for non-linear Gaussian functionals with non-Gaussian tails.
method Prove generalised Transportation-Cost Inequalities (TCIs) for specific functionals.
result Extended TCIs for rough volatility and Parabolic Anderson Model.