The paper revisits expected signatures in semimartingale models, providing new formulae and simplifying complexity.
problem Computing expected signatures in semimartingale models.
method Revisits and provides new formulae for computing expected signatures in a general semimartingale setting.
result Log-transform of expected signatures simplifies complexity, leading to signature cumulants.
Paper introduces branched signature model for efficient computation and data-driven applications.
problem Efficient computation and data-driven modeling of branched rough paths.
method Develops a universal approximation theorem and constructs an extension map to realize branched signatures.
result Explicit construction of branched signatures via an extension map for efficient computation.
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.
Path signatures improve hedging of exotic derivatives in non-Markovian models.
problem Hedging exotic derivatives under non-Markovian stochastic volatility models.
method Investigates path signatures in deep and shallow learning contexts, comparing neural networks and regression approaches.
result Path signatures outperform LSTM in most cases and yield more accurate results in hedging.
Deep signature/log-signature FBSDE algorithm improves accuracy and training time.
problem Solving FBSDEs with state and path dependent features.
method Incorporates deep signature/log-signature transformation into RNN model.
result Improves accuracy and training time compared to existing methods.
Develops a new family of signature-changing models on metric manifolds.
problem Signature changes in metric manifolds.
method One-parameter family of Lorentz-Riemann models, local expressions around change.
result Generalizes existing signature-changing models.
Universal approximation for rough paths and Lévy processes.
problem Approximating continuous functionals of càdlàg paths.
method Linear functionals of time-extended signatures.
result Universal approximation theorem for continuous functionals of càdlàg paths.
We present a novel method for extracting cancer signatures by applying statistical risk models (http://ssrn.com/abstract=2732453) from quantitative finance to cancer genome data. Using 1389 whole genome sequenced samples from 14 cancers, we identify an "overall" mode of somatic mutational noise. We give a prescription …
New method uses randomised signatures for generating financial time series data.
problem Generating synthetic financial time series data accurately.
method Introduced a Wasserstein-type distance based on discrete-time randomised signatures.
result Demonstrated universal approximation for randomised signatures on continuous functions.
Scalable machine learning with path signatures for time series and graphs.
problem Challenges in real-world time series and graph data.
method Combines rough path theory with probabilistic, deep, and kernel methods.
result Scalable models for time series and graph data.
pySigLib speeds up signature-based computations on CPUs and GPUs.
problem Efficient signature-based computations on large datasets and long sequences.
method Optimised Python library for CPU and GPU, novel differentiation scheme.
result Accurate gradients at a fraction of the runtime of existing libraries.
New imputation strategies improve signature models for irregular time series.
problem Applying signature models to irregular time series requires continuous path construction.
method Characterized imputation as a problem, evaluated various strategies, proposed GP-PoM.
result Gaussian process adapters improve predictive performance and robustness.
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.
Framework uses optimal transport to quantify model risk in stochastic path laws.
problem Model risk in stochastic path laws.
method Signature-induced optimal transport framework.
result Explicit robust bounds and budget-aware sparse surrogate method.
In the algebraic context, we show that null Osserman, spacelike Osserman, and timelike Osserman are equivalent conditions for a model of signature (2,2). We also classify the null Jordan Osserman models of signature (2,2). In the geometric context, we show that a pseudo-Riemannian manifold of signature (2,2) is null Jo…
Study on martingale property and moment explosions in signature volatility models.
problem Analyzing the martingale property and moment explosions in signature volatility models.
method Fine analysis of the explosion time of a signature stochastic differential equation.
result The price process is a true martingale if and only if the order of the linear form is odd and a correlation parameter is negative.
The model uses signatures to accurately calibrate SPX and VIX options without jumps or rough volatility.
problem Joint calibration of SPX and VIX options without jumps or rough volatility.
method The approach uses a stochastic volatility model with signatures of polynomial diffusions to price and calibrate SPX and VIX options.
result Highly accurate calibration results for SPX and VIX options without adding jumps or rough volatility.
Researchers develop Malliavin calculus for signatures, simplifying option Greeks computation.
problem Lack of tractability and explicit representations in Malliavin calculus.
method Focus on finite linear combinations of time-extended Brownian motion signatures, derive explicit formulas for Malliavin derivative, and compute Greeks for path-dependent options.
result Closed-form expressions for classical operators of Malliavin calculus, providing algebraic formulations.
The Kashaev conjecture is proven for classical signatures and Alexander polynomials of links.
problem Proving the Kashaev conjecture for signatures and Alexander polynomials.
method Relating Kashaev's matrix to Gordon-Litherland's work and Kauffman's model.
result Proven Alexander polynomial and classical signature parts of the conjecture for arbitrary links, and full conjecture for definite knots.
Generative model for TPPs using signatures and distributional discrepancies.
problem Limitations of signature methods for TPPs and lack of global sequence-level loss in neural models.
method Introduce interarrival embedding to lift jump paths to continuous paths of bounded variation, enabling signature methods for discrete event sequences. Develop sigTPP, a signature-based generative model trained on path-level loss.
result sigTPP achieves the best average rank across multiple metrics and outperforms or is within a standard error of the strongest baseline in 64% of dataset-metric pairs.
The signature is an infinite graded sequence of statistics known to characterise a stream of data up to a negligible equivalence class. It is a transform which has previously been treated as a fixed feature transformation, on top of which a model may be built. We propose a novel approach which combines the advantages o…
Signature volatility models are analyzed for existence, arbitrage, completeness, and hedging-error decomposition.
problem Existence, arbitrage, completeness, and hedging-error decomposition of signature volatility models.
method Global existence and uniqueness of strong solutions, asset-pricing, market completeness, and hedging-error decomposition derived through structural results.
result Signature volatility models are structurally sound with existence, arbitrage, completeness, and hedging-error decomposition.
Defines knot signature invariant using G-signature theorem.
problem No specific problem stated; focuses on knot theory.
method Uses G-signature theorem to define knot invariant.
result Defines an invariant for strongly invertible knots.
Develops a new trading strategy for statistical arbitrage with path-dependent signals.
problem Optimal execution in statistical arbitrage strategies with dynamic predictive signals.
method Signature-based framework modeling alpha and trading speed as linear functionals of truncated signature of market path.
result Fitted policy achieves higher return on turnover compared to a z-score benchmark.
SigMA uses signatures and attention to estimate parameters in fBm-driven SDEs.
problem Estimating parameters in SDEs driven by fBm is challenging due to non-Markovian and semimartingale issues.
method SigMA integrates path signatures with multi-head self-attention, using convolutional and MLP layers.
result SigMA outperforms other methods in accuracy, robustness, and model compactness.
Expected signatures map data streams to lower dimensions, improving ML performance.
problem Leveraging model-free embeddings for domain-agnostic machine learning.
method Expected signatures map data streams to lower dimensions, with convergence results bridging empirical and theoretical estimators.
result A modified expected signature estimator with lower mean squared error for martingale processes.
Transformer model improves asset allocation by unifying forecasting and optimization.
problem Separation of forecasting and optimization leads to suboptimal portfolios.
method Signature Informed Transformer using path signatures and specialized attention.
result Direct minimization of Conditional Value at Risk improves performance.
Introduces Exponentially Weighted Signature for better path representation.
problem Uniform treatment of historical information in signatures.
method Generalizes EFM signature to bounded linear operators, enabling contextualised temporal weighting.
result EWS is the unique solution to a linear controlled differential equation and generalizes state-space models.
New method uses path signatures for efficient likelihood estimation in time-series data.
problem Intractable likelihood functions in complex dynamic models.
method Kernel classifier based on path signatures for sequential data.
result Path signatures yield highly performant classifiers, even with low sample numbers.
A well-known property of the signature of closed oriented 4n-dimensional manifolds is Novikov additivity, which states that if a manifold is split into two manifolds with boundary along an oriented smooth hypersurface, then the signature of the original manifold equals the sum of the signatures of the resulting manifol…
Maximum Levine-Tristram signature of torus knots follows a reduction formula.
problem Determining the maximum Levine-Tristram signature for torus knots.
method Proved a reduction formula analogous to Gordon-Litherland-Murasugi's classical signature result.
result Maximum Levine-Tristram signature of torus knots satisfies a reduction formula.
New findings on mesh group-planes validate Signature-inverse Theorem under specific conditions.
problem Invalidity of existing inverse theorems for mesh group-planes.
method Classification of three and five point meshes, analysis of joint invariant signatures.
result Valid conditions for the Signature-inverse Theorem in mesh group-planes.
Signature kernel scoring rule improves weather forecasting by capturing temporal and spatial dependencies.
problem Lack of suitable scoring rules for probabilistic weather forecasting.
method Reframe weather variables as continuous paths using iterated integrals (signature kernels) to capture temporal and spatial dependencies.
result Signature kernel scoring rule outperforms conventional methods in weather forecasting, especially for long-term forecasts.
Study of 4D symmetric spaces with (2,2) signature.
problem Existence and non-existence of compact quotients.
method Analysis of pseudo-Riemannian symmetric spaces with signature (2,2).
result Solved the problem of compact quotients existence.
Introduces flat discrete signatures for financial data analysis.
problem Representing financial data for machine learning without continuous transformation.
method Introduced flat discrete signatures and discrete signatures, generalizing flat discrete signatures.
result Flat discrete signatures can represent quadratic variation relevant in finance.
The area of Handwritten Signature Verification has been broadly researched in the last decades, but remains an open research problem. In offline (static) signature verification, the dynamic information of the signature writing process is lost, and it is difficult to design good feature extractors that can distinguish g…
The study identifies volatility models from path geometry using signature-based methods.
problem Identifying different stochastic volatility models from observed data.
method Mapping volatility trajectories into a feature space via truncated path signatures and applying a gradient boosting classifier.
result The method achieves high classification accuracy across various volatility dynamics and parameter settings.
This is a sequel to the paper "The signature package on Witt spaces, I. Index classes" by the same authors. In the first part we investigated, via a parametrix construction, the regularity properties of the signature operator on a stratified Witt pseudomanifold, proving, in particular, that one can define a K-homology …
A new neural network model reduces features in high-dimensional sequential data.
problem Exponential growth in features of truncated signature transform in high-dimensional data.
method Proposes a neural network model inspired by Convolutional Neural Networks to address feature growth.
result Reduces the number of features efficiently in a data-dependent way.
We define the Analytical signature, the Hodge signature and the de Rham signature for a foliated manifold with boundary with foliation transverse to the boundary. We show that all these signatures coincide and a Hirzebruch formula is valid.
Generalizes global hyperbolicity to higher signatures and proves compactness.
problem Global hyperbolicity in higher pseudo-Riemannian signatures.
method Generalization and proof of compactness of causal diamonds.
result Existence of solutions to a Plateau problem and characterization of holonomies.
The paper examines the consistency of Lasso regression applied to signature analysis of time series data.
problem Consistency of Lasso regression in signature analysis of time series data.
method The paper studies the consistency of Lasso regression applied to signature analysis of time series data, both theoretically and numerically.
result The Lasso regression is consistent both asymptotically and in finite sample for certain types of time series and processes.
Study signatures of torus links and their cores using Neumann's equivariant signatures and Hirzebruch's formula.
problem Computing signatures of torus links and their cores.
method Use Neumann's equivariant signatures and rewrite Hirzebruch's formula for torus links (without cores) in terms of integral points in a parallelogram.
result Rewritten Hirzebruch's formula for torus links with cores using integral points in a parallelogram.
This paper extends the C*-signature to non-Witt spaces using noncommutative geometric methods.
problem Extending the signature to non-Witt spaces with noncommutative geometric methods.
method Noncommutative geometric methods, combinatorial framework, and comparison with analytical signature.
result Constructing the C*-signature on non-Witt spaces.
Paper generalizes path signature using fractional calculus for improved machine learning.
problem Improving path signature for machine learning applications.
method Introduces two new signatures inspired by fractional calculus and machine learning considerations.
result Significant accuracy improvements in handwritten digit recognition.
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.
Paper uses algebraic signatures to identify probabilistic structures in empirical data.
problem Identifying probabilistic structure from observed binomials in empirical probability tensors.
method Treating vanishing binomials as algebraic signatures, matching signatures to identify models without parameter estimation.
result The method successfully identified rank-one structures in real language data, revealing interpretable sets of words.
New method solves optimal stopping problems using rough path signatures.
problem Optimal stopping problems in finance and other fields.
method Using rough path signatures and deep neural networks.
result Solves optimal stopping problems efficiently under minimal assumptions.