Novel framework discovers SPDEs from limited data.
problem Discovering SPDEs from limited data.
method Combines stochastic calculus, variational Bayes, and sparse learning.
result Accurately identifies SPDEs from limited data.
On-device research index
arXiv research
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.
168,695 papers · 148 categories
Trend · papers per month
48 results for “SPDEs”
The paper examines conditions for stochastic invariance of cones in SPDEs with jumps.
problem Stochastic invariance of cones in SPDEs with jumps.
method Sufficient conditions for stochastic invariance of closed convex cones in abstract -spaces.
result Conditions for stochastic invariance of cones are provided and analyzed.
Improved Gaussian process inference for spatio-temporal data.
problem Cubic computational costs in Gaussian process inference, especially in spatio-temporal settings.
method Proposes the Vanilla-SPDE Exchange, leveraging an equivalence between standard and SPDE formulations to achieve improved computational cost.
result Demonstrates improved computational efficiency through complexity analysis and numerical experiments.
Conservative SPDEs emerge from fluctuating SGD dynamics in neural networks.
problem Understanding the convergence of stochastic gradient descent to SPDEs.
method Mean-field analysis and central limit theorem for SPDEs.
result Optimal convergence rates for SPDEs derived from SGD.
Deep learning based numerical approximation algorithms for stochastic partial differential equationsmath.NA
Deep learning approximates SPDE solutions from noise trajectories.
problem Approximating solutions to stochastic partial differential equations (SPDEs).
method Uses neural networks to approximate SPDE solutions based on noise realizations.
result Accurately estimates SPDE solutions and functionals like mean and variance.
Neural networks solve SPDEs using Wiener chaos expansion.
problem Solving stochastic partial differential equations (SPDEs) numerically.
method Using neural networks in the truncated Wiener chaos expansion.
result Approximation rates for learning SPDE solutions with noise.
Bayesian nonparametric models get better posterior estimates via SPDE methods.
problem Estimating posterior distributions in nonparametric Bayesian models.
method Extending diffusion methods to SPDEs on Hilbert spaces for posterior contraction and Laplace approximation.
result Derivation of posterior contraction rates and finite-sample Bernstein von Mises results.
A new method uses SPDEs to efficiently model random fields on complex domains.
problem Efficient representation of random fields on complex domains for engineering and machine learning.
method Uses SPDEs to develop a scalable framework for statFEM and GP regression.
result Can model anisotropic, non-stationary random fields with arbitrary smoothness.
New methods solve SPDEs for financial derivative pricing.
problem Deriving the price of financial derivatives using SPDEs.
method Developed a conditional Feynman-Kac formula to solve SPDEs.
result Established new numerical methods for mixed Monte-Carlo PDEs.
New graph kernels capture spatio-temporal interactions.
problem Lack of justified spatio-temporal graph kernels for graph problems.
method Derive graph kernels via SPDEs for spatio-temporal modelling.
result Non-separable spatio-temporal graph kernels outperform existing ones.
Adaptive learning of SPDE solutions using score-based diffusion models.
problem Model errors and reduced accuracy in SPDE solutions due to incomplete physical knowledge and environmental variability.
method Score-based diffusion models with recursive Bayesian inference, incorporating simulation data and observational information.
result Accuracy and robustness of the proposed method demonstrated on benchmark SPDEs.
We consider systems of diffusion processes ("particles") interacting through their ranks (also referred to as "rank-based models" in the mathematical finance literature). We show that, as the number of particles becomes large, the process of fluctuations of the empirical cumulative distribution functions converges to t…
In this article, we propose a Milstein finite difference scheme for a stochastic partial differential equation (SPDE) describing a large particle system. We show, by means of Fourier analysis, that the discretisation on an unbounded domain is convergent of first order in the timestep and second order in the spatial gri…
SON learns SPDE solutions and uncertainty from noisy data.
problem Uncertainty quantification in SPDEs with unknown model uncertainties.
method Combining DeepONet and SNNs, SON models stochasticity and predicts uncertainty.
result SON accurately captures solution structure and quantifies predictive uncertainty.
Paper improves CDO calibration using Magnus Expansion and Deep Learning.
problem Calibrating CDO to iTraxx market data.
method Large basket approximation, SPDE, Magnus expansion, Deep Learning.
result Highly accurate calibration to market data.
We propose a dynamic mean field model for `systemic risk' in large financial systems, which we derive from a system of interacting diffusions on the positive half-line with an absorbing boundary at the origin. These diffusions represent the distances-to-default of financial institutions and absorption at zero correspon…
Study well-posedness of SPDE on Riemannian manifolds with rough initial conditions.
problem Well-posedness of parabolic Anderson model on Riemannian manifolds with rough initial conditions.
method Construct intrinsic Gaussian noises, explore global geometry, use Feynman-Kac formula.
result Show well-posedness with non-positive curvature and conditions on .
Exchange uses incentives to optimize limit order book dynamics.
problem Optimizing market liquidity in fragmented electronic markets.
method Modeling limit order book as SPDE and using control theory to design incentives.
result Exchange can design incentives to modify order book shape and increase liquidity.
We link SVEs to SPDEs and derive Kolmogorov equations for singular kernels.
problem Solving stochastic Volterra equations with singular kernels.
method Establishing connections between SVEs and SPDEs, using stochastic calculus in Hilbert spaces.
result Solutions of SVEs can be expressed in terms of backward Kolmogorov equations.
Derives new equations for stochastic volatility models.
problem Modeling local-stochastic-volatility models and their derivatives.
method Conditional forward equation, Dupire stochastic PDE, rolling expiry vanilla option SPDE.
result New equations for LSV models and their derivatives.
Model for high-frequency trading with rough volatility.
problem High-frequency trading dynamics and rough volatility modeling.
method Stochastic partial differential equation (SPDE) with rough volatility driven by a Hawkes process.
result The volatility path of the SPDE is rougher than that driven by a standard Brownian motion.
Neural architecture improves geophysical data assimilation with uncertainty quantification.
problem Improving geophysical data interpolation with uncertainty quantification.
method Neural variational data assimilation with SPDE priors.
result Demonstrated improved performance and uncertainty quantification.
We consider a stochastic model for the dynamics of the two-sided limit order book (LOB). Our model is flexible enough to allow for a dependence of the price dynamics on volumes. For the joint dynamics of best bid and ask prices and the standing buy and sell volume densities, we derive a functional limit theorem, which …
We prove a law of large numbers for the loss from default and use it for approximating the distribution of the loss from default in large, potentially heterogenous portfolios. The density of the limiting measure is shown to solve a non-linear SPDE, and the moments of the limiting measure are shown to satisfy an infinit…
The paper develops methods to price options under rough volatility models using BSPDEs.
problem Pricing options in models with non-Markovian dynamics.
method Backward stochastic partial differential equations (BSPDEs) and deep learning for numerical approximations.
result Existence and uniqueness of weak solutions for general nonlinear BSPDEs.
In Bender and Dokuchaev (2013), we studied a control problem related to swing option pricing in a general non-Markovian setting. The main result there shows that the value process of this control problem can be uniquely characterized in terms of a first order backward SPDE and a pathwise differential inclusion. In the …
Positivity of mild solution to stochastic evolution equations with an application to forward ratesmath.AP
We prove a maximum principle for mild solutions to stochastic evolution equations with (locally) Lipschitz coefficients and Wiener noise on weighted spaces. As an application, we provide sufficient conditions for the positivity of forward rates in the Heath-Jarrow-Morton model, considering the associated Musiela …
We consider an SPDE description of a large portfolio limit model where the underlying asset prices evolve according to certain stochastic volatility models with default upon hitting a lower barrier. The asset prices and their volatilities are correlated via systemic Brownian motions, and the resulting SPDE is defined o…
The purpose of this paper relies on the study of long term yield curves modeling. Inspired by the economic litterature, it provides a financial interpretation of the Ramsey rule that links discount rate and marginal utility of aggregate optimal consumption. For such a long maturity modelization, the possibility of adju…
Motivated by a zero-intelligence approach, the aim of this paper is to connect the microscopic (discrete price and volume), mesoscopic (discrete price and continuous volume) and macroscopic (continuous price and volume) frameworks for the modelling of limit order books, with a view to providing a natural probabilistic …
We establish existence, uniqueness and regularity of solution results for a class of backward stochastic partial differential equations with singular terminal condition. The equation describes the value function of non-Markovian stochastic optimal control problem in which the terminal state of the controlled process is…
New method for dynamic valuation in markets with random endowments.
problem Dynamic valuation in markets with random endowments.
method Developed new FBSDE systems and established optimality conditions.
result Established necessary and sufficient conditions for optimality.
We study a constrained optimal control problem with possibly degenerate coefficients arising in models of optimal portfolio liquidation under market impact. The coefficients can be random in which case the value function is described by a degenerate backward stochastic partial differential equation (BSPDE) with singula…
The study optimizes Gaussian process approximations for finite-rank models.
problem Posterior behavior of finite-rank approximations differs from parent GP priors.
method Locally supported basis expansions with dependent Gaussian coefficients.
result Finite-rank expansions inherit the same posterior contraction rate as parent GP priors.
Derives new equations for volatility models and option pricing.
problem Modeling and pricing options in local-stochastic-volatility models.
method Develops conditional forward equations and Dupire stochastic PDEs.
result Derives new SPDE for vanilla options.
New deep learning method approximates Benes filter model.
problem Approximating high-dimensional SPDEs for filtering.
method Deep learning mesh-free neural network representation.
result First study of neural network method for Benes model.
Approximating Gaussian Whittle-Matern Fields over Well-Centered Triangulations of Riemannian Manifolds
problem Convergent approximation of Gaussian Whittle-Matern fields on Riemannian manifolds
method Finite Element approximation of SPDEs
result Universal approximation of precision and covariance matrices
Unified framework models multiple financial and insurance term structures.
problem Modeling multiple term structures in various markets.
method Extended Heath-Jarrow-Morton (HJM) approach under real-world probability.
result Characterization of local martingale deflators and existence of affine realizations.
PASTIS method selects simple models from noisy data.
problem Selecting correct models from large candidate libraries.
method PASTIS (Parsimonious Stochastic Inference) using extreme value theory.
result PASTIS outperforms other methods in model identification and predictive capability.
Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantificationphysics.comp-ph
State-of-the-art computer codes for simulating real physical systems are often characterized by a vast number of input parameters. Performing uncertainty quantification (UQ) tasks with Monte Carlo (MC) methods is almost always infeasible because of the need to perform hundreds of thousands or even millions of forward m…
Degenerate backward SPDEs in domains: non-local boundary conditions and applications to financemath.PR
Backward stochastic partial differential equations of parabolic type in bounded domains are studied in the setting where the coercivity condition is not necessary satisfied and the equation can be degenerate. Some generalized solutions based on the representation theorem are suggested. In addition to problems with a st…
We conduct a study of the aliased spectral densities of Matérn covariance functions on a regular grid of points, providing clarity on the properties of a popular approximation based on stochastic partial differential equations; while others have shown that it can approximate the covariance function well, we find that i…
One of the open problems in scientific computing is the long-time integration of nonlinear stochastic partial differential equations (SPDEs). We address this problem by taking advantage of recent advances in scientific machine learning and the dynamically orthogonal (DO) and bi-orthogonal (BO) methods for representing …
Study shows how market firm capitalization models converge to stochastic PDE solutions.
problem Understanding convergence of rank-based models with common noise to stochastic PDE solutions.
method Analysis of mean field limit, martingale problem, and pathwise entropy solutions.
result Empirical cumulative distribution function converges to solution of a stochastic PDE under certain conditions.
Moving boundary problems allow to model systems with phase transition at an inner boundary. Driven by problems in economics and finance, in particular modeling of limit order books, we consider a stochastic and non-linear extension of the classical Stefan-problem in one space dimension, where the paths of the moving in…
The paper studies derivative asset analysis in structural credit risk models where the asset value of the firm is not fully observable. It is shown that in order to compute the price dynamics of traded securities one needs to solve a stochastic filtering problem for the asset value. We transform this problem to a filte…
We propose an analytically tractable class of models for the dynamics of a limit order book, described through a stochastic partial differential equation (SPDE) with multiplicative noise for the order book centered at the mid-price, along with stochastic dynamics for the mid-price which is consistent with the order flo…
Unified approach solves Kyle model with dynamic information.
problem Solving a generalized Kyle model with dynamic information.
method Monge-Kantorovich duality and backward stochastic partial differential equations.
result Characterization of optimal strategies and pricing rules.