The paper develops methods to price and hedge options in path-dependent stock models.
problem Pricing and hedging options under complex stock models.
method Develops a path-dependent PDE for option pricing and differentiability of path-dependent SDE solutions.
result Provides formulas for option Greeks and differentiability of path-dependent SDE solutions.
Extend classical theory of affine processes to path-dependent setting
problem Path-dependent affine processes
method Introduce path-dependent coefficients and provide analytic formulas for their Fourier--Laplace transform
result Define path-dependent affine processes through their exponential-affine Fourier--Laplace transform and establish a characterization theorem
Proposes a novel path generation and evaluation method for video games.
problem Generating and evaluating realistic navigation paths for video games.
method Combines nonparametric model-free transformations and copula models.
result Demonstrates precise and interpretable generation of diverse navigation paths.
A new method predicts future paths using a Monte-Carlo approach.
problem Predicting future financial paths given historical data.
method Path Shadowing Monte-Carlo method using maximum entropy model.
result Yields state-of-the-art predictions for future volatility and option smiles.
The paper calculates sensitivities for financial derivatives using path weighting methods.
problem Computing sensitivities for path-dependent financial derivatives with high variance and degeneracy issues.
method Proposes explicit path weighting formula, variance reduction adjustment, and covariance inflation technique.
result Effective methods to address high variance and degeneracy in sensitivities computation.
Paper presents a copula-based method to efficiently generate correlated sample paths from multi-step time series models.
problem Generating realistic correlation structures in multi-step forecast sample paths is expensive and time-consuming.
method Copula-based approach to generate correlated sample paths in one forward pass.
result Improved sample path quality and significant speedup over autoregressive sampling.
Although various linear log-distance path loss models have been developed, advanced models are requiring to more accurately and flexibly represent the path loss for complex environments such as the urban area. This letter proposes an artificial neural network (ANN) based multi-dimensional regression framework for path …
New probability path model improves flow matching forecasting performance.
problem Impact of probability path model selection on flow matching forecasting performance.
method Proposed a novel probability path model designed to improve forecasting performance.
result Our model achieves faster convergence during training and improved predictive performance compared to existing models.
Flow Matching enables robust training of CNFs with various probability paths.
problem Training Continuous Normalizing Flows (CNFs) at large scales.
method Flow Matching (FM) is a simulation-free approach for training CNFs by regressing vector fields of conditional probability paths.
result Flow Matching with diffusion paths yields more robust and stable training compared to diffusion-based methods.
The study compares different game-theoretic attribution methods and finds that interventional Shapley values yield less consistent results than Aumann-Shapley due to path symmetry.
problem Investigating the influence of path choice on game-theoretic attribution algorithms.
method Comparative analysis of interventional Shapley values and Generalized Integrated Gradients (GIG) methods.
result Interventional Shapley values yield less consistent attributions than Aumann-Shapley due to path symmetry and extended away from the training data manifold.
Path-dependent PDEs model VIX and Realised Variance options.
problem Modeling volatility derivatives with path-dependence.
method Continuous stochastic volatility model with Gaussian Volterra process, proving well-posedness of PDEs.
result Formulae for greeks and implied volatility provided, finite-dimensional pricing PDEs obtained in Markovian models.
This paper optimizes paths for generative models using kinetic energy.
problem Improving generative model performance and sample quality.
method Investigating and optimizing Gaussian probability paths with kinetic energy.
result Kinetic optimal Gaussian paths simplify particle trajectories and improve model performance.
Path-independent equilibrium models improve network performance on harder problems.
problem Improving network performance on harder problem instances.
method Investigated path-independent equilibrium models and their impact on network performance.
result Path independence correlates with better performance on harder problem instances.
Paper proposes method for generating paths of stochastic volatility CGMY process for option pricing.
problem Generating accurate sample paths for stochastic volatility models for option pricing.
method Monte-Carlo method for European and American options, least square regression for calibration.
result Calibrated model parameters to S\&P 100 index options market using path-dependent options.
Recently, researchers have started decomposing deep neural network models according to their semantics or functions. Recent work has shown the effectiveness of decomposed functional blocks for defending adversarial attacks, which add small input perturbation to the input image to fool the DNN models. This work proposes…
New method uses LSTM and signature theory to solve complex financial PDEs.
problem Solving path-dependent PDEs for financial derivatives pricing.
method Combining LSTM networks and rough paths theory.
result Efficient algorithms for pricing and hedging path-dependent derivatives.
We solve the paradox of score-based methods by minimizing path variance.
problem Score-based methods are path-dependent, leading to inaccurate and unstable estimators.
method Propose MVP Principle to minimize path variance, derive closed-form expression, and use flexible Kumaraswamy Mixture Model.
result Establishes new state-of-the-art results on challenging benchmarks.
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.
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.
Introduces q-paths for generalizing geometric annealing paths in machine learning.
problem Limited applicability of existing path methods in machine learning.
method Develops a family of paths derived from a generalized mean, including geometric and arithmetic mixtures.
result Empirical gains in Bayesian inference and generative model evaluation.
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.
In this thesis, we study the problem of feature learning on heterogeneous knowledge graphs. These features can be used to perform tasks such as link prediction, classification and clustering on graphs. Knowledge graphs provide rich semantics encoded in the edge and node types. Meta-paths consist of these types and abst…
We give a pragmatic/pedagogical discussion of using Euclidean path integral in asset pricing. We then illustrate the path integral approach on short-rate models. By understanding the change of path integral measure in the Vasicek/Hull-White model, we can apply the same techniques to "less-tractable" models such as the …
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.
In this paper, we introduce and develop the theory of semimartingale optimal transport in a path dependent setting. Instead of the classical constraints on marginal distributions, we consider a general framework of path dependent constraints. Duality results are established, representing the solution in terms of path d…
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.
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.
New AI method generates SDE paths without explicit coefficients.
problem Simulating unknown Markovian SDEs with limited data.
method Uses conditional diffusion models on sample paths.
result Consistently outperforms alternative methods in KL divergence.
Study path geometries with constant torsion and cone structures.
problem Characterizing path geometries with nontrivial torsion.
method Introducing constant torsion, establishing correspondence with cone structures, describing in terms of integrable systems.
result Path geometries with constant torsion correspond to cone structures on homogeneous ruled surfaces.
New algorithm speeds up path computation for optimal models.
problem Finding the exact path of optimal models from a finite set.
method Dynamic programming approach for linear time computation.
result Dynamic programming achieves linear time for breakpoints computation.
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.
New method generates realistic financial price paths with drawdowns.
problem Lack of realistic drawdown scenarios in financial simulations.
method Variational autoencoder with drawdown reconstruction loss and path signatures.
result Simulated paths closely match empirical drawdown data.
The paper provides an efficient method to price path-dependent derivatives using multiscale stochastic volatility models.
problem Pricing path-dependent derivatives under multiscale stochastic volatility models.
method Derives a Malliavin representation for the first-order approximation of the price of path-dependent derivatives.
result An efficient Monte Carlo approximation for pricing path-dependent derivatives is derived.
Proposes an efficient shrinkage path for ridge regression.
problem Ill-conditioned data in linear models.
method A new generalized ridge regression shrinkage path that minimizes MSE risk.
result The path is as short as possible while maintaining optimal trade-off.
Proposes Geodesic Integrated Gradients (GIG) for more accurate feature attributions in deep networks.
problem Flawed attributions using straight paths from Integrated Gradients (IG).
method Introduces a model-induced Riemannian metric and computes attributions along geodesics.
result GIG produces more faithful attributions than IG on benchmarks.
Modern navigation services often provide multiple paths connecting the same source and destination for users to select. Hence, ranking such paths becomes increasingly important, which directly affects the service quality. We present PathRank, a data-driven framework for ranking paths based on historical trajectories us…
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.
New method observes learning paths to improve model supervision.
problem Improving model performance through better supervision.
method Observing learning paths to refine labels and propose Filter-KD.
result Models can refine bad labels through a 'zig-zag' learning path.
LOV model calibrates European and American options with path-dependent volatility.
problem Calibrating European and American options with path-dependent volatility.
method Designing a local volatility model that incorporates path-dependent shocks through an occupation sensitivity function.
result LOV model successfully calibrates options chains with automatic European vanilla option calibration and path-dependent flexibility.
In this paper we use a time-evolving graph which consists of a sequence of graph snapshots over time to model many real-world networks. We study the path classification problem in a time-evolving graph, which has many applications in real-world scenarios, for example, predicting path failure in a telecommunication netw…
We construct algebraic and algebro-geometric models for the spaces of unparametrized paths. This is done by considering a path as a holonomy functional on indeterminate connections. For a manifold X, we construct a Lie algebroid P which serves as the tangent space to X (punctual paths) inside the space of all unparamet…
We introduce a model for the dynamics of stock prices based on a non quadratic path integral. The model is a generalization of Ilinski's path integral model, more precisely we choose a different action, which can be tuned to different time scales. The result is a model with a very small number of parameters that provid…
Rough path theory is focused on capturing and making precise the interactions between highly oscillatory and non-linear systems. It draws on the analysis of LC Young and the geometric algebra of KT Chen. The concepts and the uniform estimates, have widespread application and have simplified proofs of basic questions fr…
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.
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.
Develops path integral for spiked tensor model dynamics.
problem Dynamics of spiked tensor model with random initial conditions.
method Path integral approach applied to partial differential equations.
result Large-N saddle point equations dominated by melonic diagrams. Study lattice paths from twist knots and double twist knots.
problem Understanding combinatorics of twist knots and double twist knots.
method Analyzing quiver generating series of HOMFLY-PT polynomial limits.
result Lattice path models for twist knots and double twist knots.
A new path development layer reduces dimensionality for irregular time series.
problem High-dimensional irregular paths in machine learning.
method Finite-dimensional Lie group representations for dimension reduction.
result The development layer outperforms signature features in accuracy and dimensionality.