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.
Deep density methods improve filtering in high-dimensional systems.
New deep learning method approximates Benes filter model.
A deep learning method solves nonlinear filtering problems efficiently.
A new numerical scheme approximates nonlinear filtering densities for noisy and partial measurements.
Extends nonlinear filtering to predictable jump times.
New research connects evolutionary dynamics to Bayesian learning.
A novel method reduces dimensionality for filtering SRNs with observed variables.
Combines neural networks with splitting-up method for filtering equations.
New method improves nonlinear filtering accuracy with reduced computation.
The paper develops a computational method for efficient online filtering of diffusion processes.
This paper studies the question of filtering and maximizing terminal wealth from expected utility in a partially information stochastic volatility models. The special features is that the only information available to the investor is the one generated by the asset prices, and the unobservable processes will be modeled …
We simplify Bayesian filtering by framing it as optimization, making it practical for high-dimensional systems.
The aim of this article is to show that systems of linear partial differential equations on filtered manifolds, which are of weighted finite type, can be canonically rewritten as first order systems of a certain type. This leads immediately to obstructions to the existence of solutions. Moreover, we will deduce that th…
We use GANs and signatures to approximate conditional laws in filtering and prediction of diffusion processes.
Enhances linear regression with Kalman filter for loss minimization.
We bound the symmetry algebra of a vector distribution, possibly equipped with an additional structure, by the corresponding Tanaka algebra. The main tool is the theory of weighted jets.
In this manuscript we introduce numerical Gaussian process Kalman filtering (GPKF). Numerical Gaussian processes have recently been developed to simulate spatiotemporal models. The contribution of this paper is to embed numerical Gaussian processes into the recursive Kalman filter equations. This embedding enables us t…
Kernel learning FBSDE filter improves nonlinear filtering efficiency.
Novel filter uses deep BSDE for nonlinear density approximation.
Improved method using filtered PDEs for robust physics-informed deep learning.
We formulate probabilistic numerical approximations to solutions of ordinary differential equations (ODEs) as problems in Gaussian process (GP) regression with non-linear measurement functions. This is achieved by defining the measurement sequence to consist of the observations of the difference between the derivative …
This paper learns state, dynamics, and filtering algorithms together for data assimilation.
We consider optimal investment problems for a diffusion market model with non-observable random drifts that evolve as an Ito's process. Admissible strategies do not use direct observations of the market parameters, but rather use historical stock prices. For a non-linear problem with a general performance criterion, th…
New method combines ODE solvers with Bayesian inference for efficient model training.
In this paper we introduce a projection method for the space of probability distributions based on the differential geometric approach to statistics. This method is based on a direct L2 metric as opposed to the usual Hellinger distance and the related Fisher Information metric. We explain how this apparatus can be used…
This paper proves long-time accuracy of ensemble Kalman filters for chaotic and machine-learned systems.
A new method reduces high-dimensional filtering to quadratic complexity.
Study of filtering and smoothing in submanifolds of Euclidean space.
Develops state-space deep Gaussian processes for irregular signals.
This paper considers a non-Markov control problem arising in a financial market where asset returns depend on hidden factors. The problem is non-Markov because nonlinear filtering is required to make inference on these factors, and hence the associated dynamic program effectively takes the filtering distribution as one…
We examine some differential geometric approaches to finding approximate solutions to the continuous time nonlinear filtering problem. Our primary focus is a new projection method for the optimal filter infinite dimensional Stochastic Partial Differential Equation (SPDE), based on the direct L2 metric and on a family o…
This paper investigates optimal trading strategies in a financial market with multidimensional stock returns where the drift is an unobservable multivariate Ornstein-Uhlenbeck process. Information about the drift is obtained by observing stock returns and expert opinions. The latter provide unbiased estimates on the cu…
An important problem in fiber-optic communications is to invert the nonlinear Schrödinger equation in real time to reverse the deterministic effects of the channel. Interestingly, the popular split-step Fourier method (SSFM) leads to a computation graph that is reminiscent of a deep neural network. This observation all…
Paper tackles singularity detection in PDEs using data-driven self-supervised learning.
The paper is concerned with non-linear Gaussian filtering and smoothing in continuous-discrete state-space models, where the dynamic model is formulated as an Itô stochastic differential equation (SDE), and the measurements are obtained at discrete time instants. We propose novel Taylor moment expansion (TME) Gaussian …
New method combines ODE filters and numerical quadrature to propagate model uncertainty.
We consider the problem of maximizing expected utility for a power investor who can allocate his wealth in a stock, a defaultable security, and a money market account. The dynamics of these security prices are governed by geometric Brownian motions modulated by a hidden continuous time finite state Markov chain. We red…
We determine the Killing superalgebras underpinning field theories with rigid unextended supersymmetry on Lorentzian four-manifolds by re-interpreting them as filtered deformations of -graded subalgebras with maximum odd dimension of the Poincaré superalgebra in four dimensions. Part of this calcula…
Paper uses optimal transport for Bayesian filtering, deriving new EnKF and FPF formulations.
Unified approach to stochastic control, filtering, and stopping using rough paths.
The extended Kalman filter is perhaps the most standard tool to estimate in real time the state of a dynamical system from noisy measurements of some function of the system, with extensive practical applications (such as position tracking via GPS). While the plain Kalman filter for linear systems is well-understood, th…
Improved HGF networks avoid negative precision errors in volatility updates.
A Kalman filter reduces valuation risk in business valuation models.
A non-Euclidean generalization of conditional expectation is introduced and characterized as the minimizer of expected intrinsic squared-distance from a manifold-valued target. The computational tractable formulation expresses the non-convex optimization problem as transformations of Euclidean conditional expectation. …
This paper refines the Gaussian Sinkhorn algorithm for general multivariate models.
Develops optimal low-dimensional approximations to high-dimensional SDEs.
We study the algebraic structure of the Killing superalgebra of a supersymmetric background of -dimensional supergravity and show that it is isomorphic to a filtered deformation of a -graded subalgebra of the Poincaré superalgebra. We are able to map the classification problem for highly supersymmetric b…
Traditional Kalman filter (KF) is derived under the well-known minimum mean square error (MMSE) criterion, which is optimal under Gaussian assumption. However, when the signals are non-Gaussian, especially when the system is disturbed by some heavy-tailed impulsive noises, the performance of KF will deteriorate serious…