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.
A new method for portfolio optimization using signature signatures to incorporate path-dependencies.
problem Traditional portfolio optimization models struggle with path-dependencies and exogenous signals.
method Signature Trading framework using rough path signatures to represent trading strategies.
result Efficient incorporation of exogenous signals and drawdown control in optimal strategies.
A new VWAP execution method using transformer and signature features.
problem Asset-specific model training and complex temporal dependencies.
method Combining transformer-based design with path signatures for capturing geometric features.
result GFT-Sig model achieves superior performance in VWAP loss metrics.
We present a method for obtaining approximate solutions to the problem of optimal execution, based on a signature method. The framework is general, only requiring that the price process is a geometric rough path and the price impact function is a continuous function of the trading speed. Following an approximation of t…
Optimal timing strategy for mean-reverting price spreads.
problem Trading price spreads with mean-reverting characteristics.
method Sequential optimal stopping framework with refined signature method.
result Precise entry and exit timings that maximize gains.
Novel signature approach for pricing and hedging path-dependent options with market frictions.
problem Pricing and hedging path-dependent options with market frictions.
method Signature approach, mean-quadratic variation criterion, non-standard infinite-dimensional Riccati equations, time-augmented signature, non-Markovian stochastic control problem.
result Effective hedging strategies in frictional markets with low-truncated signature approximations.
Develops a kernel-based framework for dynamic trading strategies.
problem Optimizing portfolios with temporal dependencies in asset dynamics.
method Parameterizes trading strategies as functions in RKHS, enabling flexible, non-Markovian approaches.
result Significantly outperforms classical Markovian methods in synthetic and market-data examples.
LLM trading agents show risk feedback can improve alignment without fine-tuning.
problem Aligning LLM trading agents with financial risk.
method TradeArena testbed, risk reports, execution simulation, memory replay.
result Risk feedback can improve alignment without fine-tuning, but not universally.
Quarter-hour market bursts predict algorithmic trading and returns in crypto futures.
problem Predicting returns in cryptocurrency futures markets using quarter-hour market bursts.
method Analysis of trade data and Autocorrelation Map to identify and quantify algorithmic trading activity.
result Quarter-hour market bursts are associated with algorithmic trading and can predict returns.
This paper begins to explore the determinants of the topological properties of the international - trade network (ITN). We fit bilateral-trade flows using a standard gravity equation to build a "residual" ITN where trade-link weights are depurated from geographical distance, size, border effects, trade agreements, and …
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.
Using a model of wealth distribution where traders are characterized by quenched random saving propensities and trade among themselves by bipartite transactions, we mimic the enhanced rates of trading of the rich by introducing the preferential selection rule using a pair of continuously tunable parameters. The biparti…
A new algorithm for high-dimensional hedging problems.
problem High-dimensional, path-dependent hedging problems.
method Signature-based algorithm using operator-valued kernels and geometric rough paths.
result Theoretical guarantees on existence and uniqueness of a global minimum.
New framework detects crypto wash trading using liquidity measures.
problem Detecting and monitoring wash trading in crypto assets.
method Developed a new framework to detect wash trading through real-time liquidity fluctuation measures.
result Joint elevation in liquidity jump and diffusion indicates wash trading in crypto assets.
Paper tackles DR problem with scalable signature-based approach.
problem Memory and computation cost issues in DR solutions.
method Signature-based features, novel distance approximator.
result Proposes scalable DR solution with reduced estimation uncertainty.
We propose the application of a high-speed maximum likelihood clustering algorithm to detect temporal financial market states, using correlation matrices estimated from intraday market microstructure features. We first determine the ex-ante intraday temporal cluster configurations to identify market states, and then st…
Market events such as order placement and order cancellation are examples of the complex and substantial flow of data that surrounds a modern financial engineer. New mathematical techniques, developed to describe the interactions of complex oscillatory systems (known as the theory of rough paths) provides new tools for…
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 proposes ExsdHawkes to model LOBs, capturing volatility dynamics.
problem Modeling volatility signature plots in LOBs with high-frequency trading dynamics.
method Extended State-Dependent Hawkes Process (ExsdHawkes) with relaxed constraints.
result ExsdHawkes uniquely reproduces volatility signature plots, identifying MLOs as catalysts.
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.
The recent framework of compressive statistical learning aims at designing tractable learning algorithms that use only a heavily compressed representation-or sketch-of massive datasets. Compressive K-Means (CKM) is such a method: it estimates the centroids of data clusters from pooled, non-linear, random signatures of …
New SigSwap model for path-dependent financial risk.
problem Managing complex, path-dependent financial risks.
method Geometry-based approach using path-signature and Signature Expected Shortfall.
result Path-dependent risks can be converted into transparent risk factors.
New approach to gravity theory sacrifices smoothness for ellipticity.
problem Developing a nonsmooth theory of gravity.
method Using a negative homogeneity p-d'Alembert operator to sacrifice linearity for ellipticity.
result Obtained a low-regularity splitting theorem.
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.
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.
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.
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 …
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.
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.
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.
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 …
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.
Efficiently computes sparse signature coefficients using kernels.
problem Lack of efficient methods for sparse signature coefficients.
method Signature kernels and PDE-based methods.
result Sparse groups of signature coefficients can be isolated effectively.
New method calculates signatures of biquotients.
problem Signature calculation for homogeneous spaces.
method Generalization of Hirzebruch's computation to biquotients.
result Signature of biquotients computed for equal rank cases.
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.
Link signature limit depends on linking matrix under specific polynomial condition.
problem Limits of Tristam-Levine signature function under precise polynomial conditions.
method Analysis of Alexander polynomial and linking matrix.
result Limit of Tristam-Levine signature at 1 determined by linking matrix under specific polynomial condition.
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.
In order to reduce signalling, traders may resort to limiting access to dark venues and imposing limits on minimum fill sizes they are willing to trade. However, doing this also restricts the liquidity available to the trader since an ever increasing quantity of orders are traded by algos in clips. An alternative is to…
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.
We prove that the signature of an even, symmetric form on a finite rank integral lattice, has signature divisible by 8, provided its associated linking form vanishes in the Witt group of linking forms. Our result generalizes the well know fact that an even, unimodular form has signature divisible by 8. We give applicat…
Paper confirms Kashaev's signature conjecture for links.
problem Proving Kashaev's conjecture about link invariants.
method Using Seifert surface definition and diagrammatic approach.
result Established Kashaev's conjecture, providing a new formula for Alexander polynomial.
The paper defines signatures for Witt spaces with boundary and proves their equality.
problem Defining and proving signatures for Witt spaces with boundary.
method Introducing de Rham and Hodge signatures, extending index theory, and using von Neumann algebras.
result Equality of de Rham and Hodge signatures on Witt spaces with boundary.
In this note, we lay the groundwork for a new approach to the problem of group-signature classification of group actions on closed Riemann surfaces. This new approach first focuses on analyzing the low level arithmetic conditions on signatures before invoking the more complicated group theory. We provide the complete f…