A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
This paper proposes a new method to learn integration schemes for complex ODEs.
Via the transverse Hilbert scheme construction, we associate a holomorphic completely integrable system to a surface endowed with a holomorphic symplectic form and a projection onto . We provide a full characterization of the completely integrable systems that arise in this way.
Study of Tannakian categories for integrable connections on Kaehler manifolds.
A new simulation method for Volterra processes improves convergence for rough kernels.
The paper compares numerical schemes for nonholonomic systems using retraction maps.
We introduce the technique combining the features of integration schemes for SDYM equations and multidimensional dispersionless integrable equations to get SDYM equations on the conformally self-dual background. Generating differential form is defined, the dressing scheme is developed. Some special cases and reductions…
Efficient simulation scheme for rough Heston model reduces computational cost.
A new method simulates square-root processes efficiently.
This paper summarizes closed-form relations for SE(3) maps and their derivatives.
Asymptotic error distribution for approximation of a stochastic integral with respect to continuous semimartingale by Riemann sum with general stochastic partition is studied. Effective discretization schemes of which asymptotic conditional mean-squared error attains a lower bound are constructed. Two applications are …
We introduce a recent symplectic integration scheme derived for solving physically motivated systems with non-separable Hamiltonians. We show its relevance to Riemannian manifold Hamiltonian Monte Carlo (RMHMC) and provide an alternative to the currently used generalised leapfrog symplectic integrator, which relies on …
Enhances HNNs for conservative systems with noisy data.
We introduce a simulation scheme for Brownian semistationary processes, which is based on discretizing the stochastic integral representation of the process in the time domain. We assume that the kernel function of the process is regularly varying at zero. The novel feature of the scheme is to approximate the kernel fu…
Study shows thresholding scheme converges for mean curvature flow of convex sets.
Efficiently simulates the Heston model with large time steps using a novel method.
ContinuousNet generalizes ResNets to continuous dynamical systems.
Paper develops a finite dimensional approximation scheme for Riemannian manifolds.
Efficiently simulates SABR model with novel sampling methods.
New integration method improves BSDE-based PDE solvers.
Segmentation maps of medical images annotated by medical experts contain rich spatial information. In this paper, we propose to decompose annotation maps to learn disentangled and richer feature transforms for segmentation problems in medical images. Our new scheme consists of two main stages: decompose and integrate. …
Research covers geometry, analysis, and integration on infinite-dimensional spaces.
We relate two notions of local error for integration schemes on Riemannian homogeneous spaces, and show how to derive global error estimates from such local bounds. In doing so, we prove for the first time that the Lie-Butcher theory of Lie group integrators leads to global error estimates.
Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower bound on the desired integral to be approximated, e.g. marginal likelihood. The lo…
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.
Consider a process, stochastic or deterministic, obtained by using a numerical integration scheme, or from Monte-Carlo methods involving an approximation to an integral, or a Newton-Raphson iteration to approximate the root of an equation. We will assume that we can sample from the distribution of the process from time…
Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves seemingly new. Asymptotically efficient schemes which attain the lower bounds a…
A new machine learning method solves high-dimensional Kolmogorov PDEs efficiently.
Developed a monotone numerical method for MV portfolio optimization under jump-diffusion models.
The paper explores reductions of self-dual conformal structure equations.
For the first time in mathematical finance field, we propose the local weak form meshless methods for option pricing; especially in this paper we select and analysis two schemes of them named local boundary integral equation method (LBIE) based on moving least squares approximation (MLS) and local radial point interpol…
New schemes for SDEs on manifolds keep solutions close to the manifold.
We review properties of so-called special conformal Killing tensors on a Riemannian manifold and the way they give rise to a Poisson-Nijenhuis structure on the tangent bundle . We then address the question of generalizing this concept to a Finsler space, where the metric tensor field comes from a regular La…
The paper efficiently solves a complex option valuation equation for two assets.
After analyzing renormalization schemes on a Poincaré-Einstein manifold, we study the renormalized integrals of scalar Riemannian invariants. The behavior of the renormalized volume is well-known, and we show any scalar Riemannian invariant renormalizes similarly. We consider characteristic forms and their behavior und…
Continues work on derived manifolds and symplectic schemes, constructing virtual classes.
Thermodynamic integration (TI) for computing marginal likelihoods is based on an inverse annealing path from the prior to the posterior distribution. In many cases, the resulting estimator suffers from high variability, which particularly stems from the prior regime. When comparing complex models with differences in a …
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear systems is obtained, and the integration scheme for such equations is proposed.
This work analyzes discrete diffusion models using stochastic integrals, providing error bounds and insights.
New integrators preserve geometric structure in Hamiltonian systems.
New simulation method simplifies Heston model with Poisson conditioning for better accuracy and efficiency.
We consider the approximation of stochastic differential equations (SDEs) with non-Lipschitz drift or diffusion coefficients. We present a modified explicit Euler-Maruyama discretisation scheme that allows us to prove strong convergence, with a rate. Under some regularity and integrability conditions, we obtain the opt…
Optimized AIS scheme reduces bias and MSE for general proposals.
Hybrid model combines continuous and tractable probabilistic models.
This paper proposes a novel scheme for the watermarking of Deep Reinforcement Learning (DRL) policies. This scheme provides a mechanism for the integration of a unique identifier within the policy in the form of its response to a designated sequence of state transitions, while incurring minimal impact on the nominal pe…
Improved speech recognition with language model integration in sequence-to-sequence models.
Novel IMEX scheme solves financial PDEs with mixed derivatives.
Adaptive quadrature improves Bayesian inference through active learning.
A new method integrates forms on Riemann surfaces, leading to modular forms.