The paper defines and analyzes set-valued stochastic integrals for Lévy processes.
problem Defining and analyzing set-valued stochastic integrals for Lévy processes.
method Extending classical definitions to convoluted integrals with square-integrable kernels, and proving properties of set-valued convoluted stochastic integrals.
result Set-valued convoluted stochastic integrals can be explosive and take extended vector values.
Constructs Lie groupoid integrating elliptic tangent bundles and Poisson structures.
problem Existence and integration of elliptic tangent bundles and Poisson structures.
method Explicit construction of Lie groupoids and local models for symplectic integration.
result Necessary and sufficient topological condition for integration of elliptic tangent bundles.
The aim of this paper is to identify the determinants of international stock markets integration. Intuitively we selected a great number of factors linked to financial integration. Then, we developed an international asset-pricing model with time-varying degree of integration. This model is estimated for 30 countries (…
TQ separates sampling and integration for high-dimensional integrals.
problem High-dimensional integration challenges in science.
method Tree Quadrature (TQ) constructs a surrogate model using regression trees.
result TQ outperforms existing methods in up to 15 dimensions.
Survey of integrable billiard models and inequalities.
problem Understanding integrable billiard dynamics.
method Analysis of various billiard models.
result Isoperimetric inequality for Mather β-function.
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 …
Two EP frameworks ensure integrable beliefs in Bayesian estimation problems.
problem Non-integrable beliefs in EP can lead to infeasible solutions.
method Proposes two EP frameworks to keep messages non-integrable.
result Ensures integrable beliefs in EP, even with non-integrable messages.
Integrates prediction models into portfolio optimization for better asset allocation.
problem Traditional portfolio optimization ignores prediction models, leading to suboptimal decisions.
method Developed a framework that combines regression prediction with mean-variance optimization, providing analytical solutions and neural-network-based optimization for inequality constraints.
result Demonstrated through simulations that integrating prediction models improves portfolio performance.
A new model DKMPP integrates covariates and uses an integration-free method for spatio-temporal point processes.
problem Training intractable deep spatio-temporal point processes with multimodal covariates.
method DKMPP uses a deep kernel to model complex relationships and an integration-free score matching method.
result DKMPP and score-based estimators outperform baseline models in spatio-temporal point processes.
Study integrability of quantized six-vertex model on torus.
problem Integrability of a specific lattice model on a torus.
method Defined layer transfer matrices and tetrahedron equations for admissible graphs.
result Established commutativity of transfer matrices and derived quantum Hamiltonians.
Integrable dynamics explained via geometric maps and cluster algebras.
problem Integrable dynamics in projective geometry.
method Twisted triple crossing diagram maps and cluster integrable systems.
result Cross-ratio dynamics described by geometric R-matrices. Unified asymptotic theory and tests for ACD models reveal infinite-mean durations in cryptocurrency trading.
problem Challenges in asymptotic theory for ACD models, especially for integrated ACD.
method Unified asymptotic theory for quasi-maximum likelihood estimator, hypothesis testing framework.
result Infinite-mean durations in cryptocurrency trading, rejected integrated ACD hypothesis.
We use neural networks as control variates with geometric integration techniques.
problem Analytic integration of neural network approximations for variance reduction.
method Integration domain subdivision using computational geometry for MLPs with continuous piecewise linear activation functions.
result Neural networks can be used as control variates with geometric integration methods.
Formalizes quantum path integrals using groupoids and differential forms.
problem Formalizing Feynman's path integral in quantum mechanics.
method Shifted focus to pair groupoid, using van Est map and piecewise linear structures.
result Developed a coordinate-free approach to integration of differential forms.
This work analyzes discrete diffusion models using stochastic integrals, providing error bounds and insights.
problem Error analysis for discrete diffusion models remains less understood.
method Proposes a comprehensive framework based on Lévy-type stochastic integrals.
result Obtains the first error bound for the τ-leaping scheme in KL divergence. For every adapted, càglàd process (strategy) G and typical càdlàg price paths whose jumps satisfy some mild growth condition we define integral G⋅S as a limit of simple integrals.
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.
We show that various notions of integrability for Poisson brackets are all equivalent, and we give the precise obstructions to integrating Poisson manifolds. We describe the integration as a symplectic quotient, in the spirit of the Poisson sigma-model of Cattaneo and Felder. For regular Poisson manifolds we express th…
We present the theory of tensors with Young tableau symmetry as an efficient computational tool in dealing with the polynomial first integrals of a natural system in classical mechanics. We relate a special kind of such first integrals, already studied by Lundmark, to Beltrami's theorem about projectively flat Riemanni…
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…
Research integrates sentiment analysis with reinforcement learning for better trading strategies.
problem Improving trading performance by integrating sentiment data.
method Developed a sentiment-driven trading system using a large language model and reinforcement learning.
result Sentiment signals from FinGPT improve trading performance when combined with technical indicators.
Improved speech recognition with language model integration in sequence-to-sequence models.
problem Improving word error rate in speech recognition models.
method Log-linear combination of acoustic and language models with per-token renormalization.
result The proposed method shows good improvements over standard model combination on Librispeech system.
Hybrid model combines continuous and tractable probabilistic models.
problem Intractable probabilistic inference in continuous latent-space models.
method Continuous mixtures of tractable probabilistic models with finite integration points.
result Hybrid models achieve state-of-the-art performance in density estimation.
Proposes a multivariate regression model for better analysis of multiple datasets.
problem Insufficient performance of single-dataset analysis in integrative studies.
method Sparse estimation for variable and group selection, alternating direction method of multipliers algorithm.
result Demonstrated improved performance through simulations and real data analysis.
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. New integrators preserve geometric structure in Hamiltonian systems.
problem Preserving geometric structure in Hamiltonian systems on Jacobi manifolds.
method Combining Poissonization and symplectic bi-realizations to construct structure-preserving integrators.
result Explicit construction and application of Jacobi Hamiltonian integrators.
Paper rigorously defines Feynman graph integrals on Kähler manifolds.
problem Establishing convergence of Feynman graph integrals on Kähler manifolds.
method Using Getzler's rescaling technique, graph integrands are extended to forms with divisorial-type singularities in the compactification of configuration spaces.
result Feynman graph integrals are rigorously defined as Cauchy principal value integrals.
A new method combines AIS and SMCI for efficient evaluation of Ising models.
problem Efficiently evaluating expectations on Ising models under various temperatures.
method Combining Annealed Importance Sampling (AIS) and Spatial Monte Carlo Integration (SMCI).
result The proposed method performs efficiently in both high- and low-temperature regions.
This research improves deep neural networks for parameter identification and prediction in stochastic Volterra integral equations.
problem Parameter identification and prediction in Volterra integral equations driven by Gaussian noise.
method Improved deep neural networks framework that incorporates inter-output relationships into the loss function.
result The framework enhances parameter estimation accuracy and provides accurate solutions for modeling stochastic systems.
Study forward investment performance in semimartingale markets with stochastic factors.
problem Investigate forward investment performance in incomplete semimartingale markets with power risk preferences and stochastic integrated factors.
method Develop necessary and sufficient conditions for FIPP existence, use integral representations, and solve ill-posed HJB equations.
result Explicit constructions for time-monotone FIPPs in semimartingale models, generalizing from Brownian to semimartingale markets.
In this paper we present the solution to a longstanding problem of differential geometry: Lie's third theorem for Lie algebroids. We show that the integrability problem is controlled by two computable obstructions. As applications we derive, explain and improve the known integrability results, we establish integrabilit…
Review of sigma models on flag manifolds, linking to spin chains and integrable theories.
problem Understanding phase transitions and anomalies in spin chains and sigma models.
method Analyzing topological angles, discrete 't Hooft anomalies, and integrable models.
result Gapless phases in certain spin chains can be explained by discrete anomalies in continuum theories.
Paper uses referenced thermodynamic integration for Bayesian model selection in a complex COVID-19 transmission model.
problem Bayesian model selection with uncertainty and misleading metrics.
method Referenced thermodynamic integration for intractable high-dimensional distributions.
result Favourable convergence performance in model selection for COVID-19 transmission.
We discuss a semi-analytical method for solving SABR-type equations based on path integrals. In this approach, one set of variables is integrated analytically while the second set is integrated numerically via Monte-Carlo. This method, known in the literature as Conditional Monte-Carlo, leads to compact expressions fun…
Bayesian quadrature uses probabilistic models for estimating intractable integrals.
problem Estimating intractable integrals in complex models.
method Probabilistic, model-based approach using Gaussian processes.
result Comprehensive review and systematic taxonomy of Bayesian quadrature methods.
A new method speeds up sampling in diffusion models.
problem Slow sample generation in diffusion models.
method Proposed Splitting Integrators for fast stochastic sampling.
result Achieved FID score of 2.36 in 100 NFE, significantly faster than baselines.
MKL-based models outperform complex multi-omics integrative approaches.
problem Integrating diverse omics data sources.
method Supervised multiple kernel learning with different kernel fusion strategies.
result MKL-based models outperform more complex architectures.
Improved path integral method for financial derivatives pricing.
problem Analytical intractability of financial derivative pricing models.
method Generalized semi-classical path integral approach to time-dependent Hamiltonians.
result Accuracy and computational efficiency of the path integral approach for derivatives pricing.
A new financial integral constructed without lattice assumptions.
problem Creating a financial integral without assuming a lattice structure.
method Weak no-arbitrage condition and properties of trajectory space.
result Integral not associated with a measure, demonstrating non-lattice integration.
In the framework of path integral the evolution operator kernel for the Merton-Garman Hamiltonian is constructed. Based on this kernel option formula is obtained, which generalizes the well-known Black-Scholes result. Possible approximation numerical schemes for path integral calculations are proposed.
Physics models integrated into VAEs improve generative performance and extrapolation.
problem Improving generative models with interpretability and robustness.
method Physics-based latent space in VAEs with regularized learning to balance physics and neural network components.
result Generative performance and extrapolation improvements demonstrated on synthetic and real-world datasets.
It is well-known that sigma-models with symmetric target spaces are classically integrable. At the example of the model with target space the flag manifold U(3)/U(1)^3 -- a non-symmetric space -- we show that the introduction of torsion allows to cast the equations of motion in the form of a zero-curvature condition fo…
Paper integrates LLMs into portfolio optimization to improve decision quality.
problem Suboptimal portfolio decisions due to mismatch between prediction and decision quality.
method Integrates LLMs with decision-focused learning, using attention mechanism to process asset relationships and macro variables.
result Model consistently outperforms state-of-the-art deep learning models in portfolio optimization.
The paper addresses numerical integration issues in SV models, proposing a fast regime switching algorithm.
problem Numerical integration challenges in SV models, especially with high precision and low computational time.
method Proposes a fast regime switching algorithm to determine when higher precision arithmetic is needed.
result Shows that numerical quadratures need to be carefully chosen based on model parameters and parameter values.
Proposes a diagnostic method to evaluate factor models using cap-axis integrals.
problem Improving factor model evaluation in low-dimensional spaces.
method Lifts pricing errors into a bridge-alpha curve along the market-capitalization rank axis.
result The cap-axis norm is distinct from Sharpe gain and size exposure.
Proposes a diagnostic method to evaluate factor models using cap-axis integrals.
problem Improving factor model evaluation for low-dimensional models.
method Lifts pricing errors into a bridge-alpha curve along the market-capitalization rank axis.
result The cap-axis norm is distinct from Sharpe gain and size exposure.
Develops integrators for Hamiltonian systems in Jacobi manifolds.
problem Modeling conservative systems with dissipative and thermodynamic phenomena.
method Constructs structure-preserving integrators for Hamiltonian systems in Jacobi manifolds.
result Proposes a numerical integration technique compatible with Jacobi dynamics.
New BdryMatérn GP model for reliable boundary integration on irregular domains.
problem Incorporating boundary information in Gaussian process models for complex phenomena.
method Proposes a novel BdryMatérn GP framework with a new covariance kernel derived via path integral and stochastic PDE.
result Sample paths from the BdryMatérn GP satisfy desired boundaries with smoothness control on derivatives.