Derives an explicit formula for optimal portfolios in financial markets.
problem Optimal investment problem in complete financial markets driven by Wiener process.
method Functional Itô calculus approach, relying only on integrability condition.
result Derives an explicit formula for the optimal portfolio process.
This paper proposes a new method to optimize portfolio allocation with transaction costs using Wiener chaos expansion.
problem Optimizing portfolio allocation with transaction costs in multi-period settings.
method Wiener chaos expansion approach to represent and solve the optimization problem.
result The proposed method finds an optimal strategy for portfolio allocation with transaction costs.
A new error bound improves safety in Bayesian optimization.
problem Ensuring safety in Bayesian optimization with probabilistic models.
method Introducing a novel error bound using Wiener kernel regression for Gaussian processes and noise.
result The new error bound provides larger safety regions than previous methods.
Paper proposes a new model for better engine control.
problem Optimal control problems are non-convex and hard to solve online.
method Combines Hammerstein-Wiener model with input convex neural networks.
result Optimal control problems are effectively solvable due to convexity and partial linearity.
Model predicts cash accumulation for assets with unknown prices.
problem Cash accumulation for assets with unpredictable future prices.
method Discretized Wiener Process matched using ordinary integrals.
result Model efficiently predicts cash accumulation for various asset scenarios.
The paper proves a convergence theorem for Wiener measures on holonomy groups.
problem Understanding convergence of Wiener measures on holonomy groups.
method Using stochastic parallel transports along convergent metric connections.
result Proves a convergence theorem for push-forward Wiener measures on holonomy groups.
Formulae prove integration by parts for foliated Wiener measure.
problem Integration by parts formula for foliated Wiener measure.
method Proved integration by parts formula for horizontal Wiener measure on totally geodesic Riemannian foliations.
result Horizontal Wiener measure has quasi-invariance under certain flows.
New linear denoiser outperforms standard Wiener filter in noisy data.
problem Improving denoising performance for unknown covariance data.
method Synthetically constructed noisy samples to train a linear denoiser using least-squares approximation.
result Optimal denoiser found using the Convex Gaussian Min-Max Theorem (CGMT) for proportional regime.
Optimal smooth subspaces approximate large data sets efficiently.
problem Approximating large data sets with invariant subspaces.
method Smooth functions under lattice translations or crystallographic groups, with optimal selection of Paley-Wiener space.
result Optimal lattice selection enhances approximation efficiency.
This is an introduction to Wiener measure and the Feynman-Kac formula on general Riemannian manifolds for Riemannian geometers with little or no background in stochastics. We explain the construction of Wiener measure based on the heat kernel in full detail and we prove the Feynman-Kac formula for Schrödinger operators…
New method calculates barrier option Greeks using Wiener path integrals.
problem Computing first-order Greeks for barrier options efficiently.
method Developed chain rules for Wiener path integrals.
result Effectiveness demonstrated through numerical examples.
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.
The paper models asset prices using Wiener chaos expansions for efficient calibration to implied volatility surfaces.
problem Calibrating to implied volatility surfaces using flexible martingale models.
method Constructing an over-parameterized martingale model based on Wiener chaos expansions and conditional expectations.
result The method enables fast calibration to implied volatility surfaces and demonstrates flexibility through numerical experiments.
New methods for Z-transform inversion and Wiener-Hopf factorization.
problem Efficient numerical inversion of Z-transforms and factorization of functions. method Sinh-deformations of contours, variable changes, and simplified trapezoid rule.
result High precision and speed in evaluating moments and constructing filters.
Paper develops a new framework for analyzing certainty equivalents and dynamic risk premia using Malliavin calculus and Wiener chaos analysis.
problem Limitations of Arrow-Pratt approximation for arbitrary sequences of vanishing risks.
method Develops a new framework based on Malliavin calculus and Wiener chaos analysis, combining Itô calculus, the Clark--Ocone representation, and the Wiener chaos decomposition.
result Establishes a unified framework linking expected utility theory, stochastic analysis, and Wiener chaos expansions, revealing higher-order certainty equivalents and dynamic risk premia.
This paper gives a rigorous interpretation of a Feynman path integral on a Riemannian manifold M with non-positive sectional curvature. A L2 Riemannian metric GP is given on the space of piecewise geodesic paths HP(M) adapted to the partition P of [0,1], whence a finite-dimensional approximation of Wiener …
This paper describes a new method of bond portfolio optimization based on stochastic string models of correlation structure in bond returns. The paper shows how to approximate correlation function of bond returns, compute the optimal portfolio allocation using Wiener-Hopf factorization, and check whether a collection o…
The paper examines Wiener process for LID estimation methods.
problem Estimating local intrinsic dimension in high-dimensional datasets.
method Investigates recent LID estimation methods from a Wiener process perspective.
result Explains how methods behave under non-ideal conditions.
New method estimates SDE parameters efficiently using WCE and SGD.
problem Parameter estimation for stochastic differential equations.
method Wiener Chaos Expansion and Stochastic Gradient Descent.
result Accurate parameter recovery from noisy observations.
Cubature on Wiener space [Lyons, T.; Victoir, N.; Proc. R. Soc. Lond. A 8 January 2004 vol. 460 no. 2041 169-198] provides a powerful alternative to Monte Carlo simulation for the integration of certain functionals on Wiener space. More specifically, and in the language of mathematical finance, cubature allows for fast…
In an abstract Wiener space setting, we constract a rigorous mathematical model of the one-loop approximation of the perturbative Chern-Simons integral, and derive its explicit asymptotic expansion for stochastic Wilson lines.
Constructs non-asymptotic confidence regions for unknown functions in RKHS.
problem Global probabilistic confidence regions for unknown functions in RKHS.
method Reduces confidence region construction to estimating RKHS norm.
result Valid confidence regions can be constructed non-asymptotically.
New algorithm prices Bermudan options using Wiener chaos expansion for non-Markovian processes.
problem Pricing Bermudan options with non-Markovian payoff processes.
method Modified Longstaff Schwartz algorithm with Wiener chaos expansion for non-Markovian settings.
result Embarrassingly parallel algorithm for efficient computation.
Algorithm for pricing American options using martingale approximations.
problem Pricing American options efficiently and accurately.
method Approximating uniformly square integrable martingales with Wiener chaos expansion, solving the dual minimization problem via sample average approximation.
result Scalable parallel implementation for multi-dimensional path-dependent options.
The paper explores Wiener-Granger causality and its computational enhancements.
problem Analyzing causal relationships between time series data.
method Detailed overview of Granger causality, historical development, and computational advancements.
result Enhanced application of Granger causality in various fields.
This paper introduces joint stationarity for time-varying graph signals, improving signal processing accuracy.
problem Lack of consideration for both time and vertex dimensions in graph-based signal processing.
method Introduces joint (time-vertex) stationarity, a scalable Wiener optimization framework for joint denoising and learning.
result Joint stationarity optimally improves signal processing accuracy, as shown by real data experiments.
Survey on heat kernels and path integrals.
problem Approximating Wiener measure on compact manifolds.
method Review of recent results on approximating Wiener measure.
result Approximation of Wiener measure by measures on spaces of piece-wise geodesics.
A new method corrects CTF and noise in cryo-EM images.
problem Restoring single particle cryo-EM images from noisy and distorted data.
method Covariance Wiener Filtering (CWF) method using the covariance matrix of projection images.
result CWF successfully corrects for CTF and noise, providing better image restoration.
New pricing methods for α-quantile and early-exercise options using Spitzer identities.
problem Pricing perpetual Bermudan and American options and α-quantile options. method Based on Spitzer identities for general Lévy processes and Wiener-Hopf method.
result Direct calculation of the optimal exercise barrier for early-exercise options.
The paper improves nonparametric confidence bands for band-limited functions.
problem Constructing nonparametric simultaneous confidence bands with nonasymptotic and distribition-free guarantees.
method Based on Paley-Wiener reproducing kernel Hilbert spaces, the paper relaxes assumptions, improves noise estimation, and tightens constraints.
result Enhanced confidence bands with improved efficiency and tighter constraints.
Wiener-Granger causality is a widely used framework of causal analysis for temporally resolved events. We introduce a new measure of Wiener-Granger causality based on kernelization of partial canonical correlation analysis with specific advantages in the context of large high-dimensional data. The introduced measure is…
Counterexample shows Ito integrand needn't be locally square integrable.
problem Ito integrand's square integrability condition is not always met.
method Provided a counterexample to Ito's Lemma's integrability condition.
result Ito integrand needn't be locally square integrable.
Paper develops a finite dimensional approximation scheme for Riemannian manifolds.
problem Integration on Riemannian manifolds.
method New finite dimensional approximation scheme motivated by categorical colimit.
result Establishes a generalization for L1-functionals on Riemannian manifolds. New method distinguishes data noise from GP uncertainty.
problem Uncertainty in kernel regression with non-Gaussian noise.
method Wiener chaos expansions for non-Gaussian noise.
result Can distinguish aleatoric from epistemic uncertainty.
Let Wi={Wi(ti),ti∈R+},i=1,2,…,d are independent Wiener processes. W={W(t),t∈R+d} be the additive Wiener field define as the sum of Wi. For any trend f in $\kHC$ (the reproducing kernel Hilbert Space of W), we derive upper and lower bounds for the boundary non-crossing proba…
Certain natural geometric approximation schemes are developed for Wiener measure on a compact Riemannian manifold. These approximations closely mimic the informal path integral formulas used in the physics literature for representing the heat semi-group on Riemannian manifolds. The path space is approximated by finite …
We prove a Paley-Wiener Theorem for a class of symmetric spaces of the compact type, in which all root multiplicities are even. This theorem characterizes functions of small support in terms of holomorphic extendability and exponential type of their (discrete) Fourier transforms. We also provide three independent new p…
Data-driven model reduction captures non-Markovian dynamics using Koopman and Mori-Zwanzig formalisms.
problem Modeling complex, non-Markovian dynamics efficiently and understanding their underlying mechanisms.
method Formulates data-driven model reduction within Koopman and Mori-Zwanzig formalisms, deriving NARMAX models from dynamical systems.
result Shows how data-driven methods can represent non-Markovian dynamics using Koopman and Mori-Zwanzig formalisms.
Develops trinomial models using cubature methods for financial derivative pricing.
problem Pricing financial derivatives in complex stochastic market models.
method Cubature methods applied to Wiener space for constructing trinomial models.
result Numerical solutions compare favorably with Black-Scholes model.
The paper creates nonparametric confidence bands for band-limited functions.
problem Estimating confidence bands for band-limited functions with finite samples and unknown noise.
method Uses Paley-Wiener reproducing kernel Hilbert spaces and gradient-perturbation methods.
result Non-asymptotic guarantees for confidence regions without assuming a parametric model.
A new method solves complex control problems with random coefficients.
problem Solving LQ McKean-Vlasov control problems with random coefficients.
method Decomposes the problem into two decoupled stochastic optimal control problems.
result The sum of optimal controls of auxiliary problems equals the original problem's optimal control.
Dual Bayesian Affine Estimators for Wiener-type state-space models
problem Estimating parameters in Wiener-type state-space models
method Fixed-point architecture combining two affine estimators
result Dual basis-parameter estimator achieves comparable parameter MSE to purely affine estimator
Reduces path integrals for interacting systems using dependent coordinates.
problem Reducing path integrals for systems with symmetry.
method Reduction procedure based on Wiener-type path integral, optimal nonlinear filtering, and projection of mean curvature vector field.
result Shows non-invariance of the measure in the path integral under reduction and generates the Jacobian.
The paper ensures positivity of solutions to stochastic equations with positive initial data.
problem Ensuring positivity of solutions to stochastic equations with positive initial data.
method Providing sufficient conditions on coefficients for positivity of mild solutions.
result Sufficient conditions for positivity of solutions to stochastic equations.
This paper considers the valuation of exotic path-dependent options in Lévy models, in particular options on the supremum and the infimum of the asset price process. Using the Wiener--Hopf factorization, we derive expressions for the analytically extended characteristic function of the supremum and the infimum of a Lév…
These notes represent a much expanded and updated version of the \textquotedblleft mini course\textquotedblright that the author gave at the ETH (Zürich) and the University of Zürich in February of 1995. The purpose of these notes is to first provide some basic background to Riemannian geometry and stochastic calculus …
Paper proves existence and uniqueness of stochastic integral.
problem Existence and uniqueness of stochastic integral with Wiener process.
method Characterizes the Ito integral through two properties: simple process calculation and convergence of squared integrands.
result Existence and uniqueness theorem for stochastic integral.
Proposes a model for identifying edges in low-rank dynamical networks.
problem Inability of conventional methods to handle low-rank dynamical networks.
method Low rank dynamical network model with causal Wiener filtering.
result Consistent method for estimating all network edges.