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.
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 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.
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.
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.
We consider a standard optimal investment problem in a complete financial market driven by a Wiener process and derive an explicit formula for the optimal portfolio process in terms of the vertical derivative from functional It^o calculus. An advantage with this approach compared to the Malliavin calculus approach is t…
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.
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.
The article is devoted to models of financial markets with stochastic volatility, which is defined by a functional of Ornstein-Uhlenbeck process or Cox-Ingersoll-Ross process. We study the question of exact price of European option. The form of the density function of the random variable, which expresses the average of…
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…
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.
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.
A new normalizing flow models continuous stochastic processes efficiently.
problem Efficient modeling of continuous stochastic processes.
method Dynamic normalizing flows driven by Wiener process.
result Rich time series model with efficient computation of likelihoods and marginals.
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.
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.
Fast method developed for pricing barrier options and joint Lévy process distributions.
problem Accurate pricing of barrier options and joint distributions in Lévy models.
method Dual space calculations, Wiener-Hopf factorization, sinh-deformations, Gaver-Wynn Rho acceleration.
result Achieves precision of 10−15 in seconds and 10−9−10−8 in fractions of a second. 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…
Develops interpretable model for latent stochastic systems from noisy data.
problem Learning interpretable models of latent stochastic dynamical systems from noisy data.
method Semi-parametric model using Gaussian process for drift, inference of latent paths with sparse variational description.
result Flexible nonparametric model of dynamics with interpretable portraits.
Starting from inhomogeneous time scaling and linear decorrelation between successive price returns, Baldovin and Stella recently proposed a way to build a model describing the time evolution of a financial index. We first make it fully explicit by using Student distributions instead of power law-truncated Lévy distribu…
In this note we apply the recently established Wiener-Hopf Monte Carlo (WHMC) simulation technique for Levy processes from Kuznetsov et al. [17] to path functionals, in particular first passage times, overshoots, undershoots and the last maximum before the passage time. Such functionals have many applications, for inst…
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.
Study on stochastic covariant derivatives in curved space-time.
problem Analyzing covariant derivatives in curved space-time under stochastic processes.
method Using Itô-Wiener processes and stochastic calculus, including Besov spaces, Schrödinger operators, and white noise.
result Developed a framework for stochastic geodesics and white noise in fractoid spaces.
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…
This research explores neural SDEs as deep latent Gaussian models in the diffusion limit.
problem Deep latent Gaussian models with time-inhomogeneous Markov chains and Gaussian perturbations.
method Develops variational inference for neural SDEs using stochastic automatic differentiation in Wiener space.
result The limiting latent object is an Itô diffusion process governed by neural nets.
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.
Research in psychology and neuroscience has successfully modeled decision making as a process of noisy evidence accumulation to a decision bound. While there are several variants and implementations of this idea, the majority of these models make use of a noisy accumulation between two absorbing boundaries. A common as…
Global stock markets exhibit exponential growth and Gaussian fluctuations with self-similar monthly patterns.
problem Understanding regularities in stock market fluctuations across different countries.
method Analysis of daily and monthly stock indices from six countries.
result Monthly stock growth is statistically self-similar to daily growth and follows a Wiener process.
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.
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.
Efficient methods for Lévy models using SINH-regular processes.
problem Efficient numerical methods for evaluating Lévy models.
method Defining SL-processes and sSL-processes, deriving properties of characteristic exponent, and showing all popular Lévy processes can be subordinated to Brownian motion.
result All crucial properties of characteristic exponent are consequences of a specific representation, and all popular Lévy processes are SL- or sSL-subordinated Brownian motion.
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.
Quantum effects improve stock option pricing model.
problem Persistent discrepancies between classical Black-Scholes model and actual stock prices.
method Introduced an additional pseudo-Wiener process to represent non-classical information.
result The norm of a complex quantity compensates for price discrepancies, providing market evidence for non-classical processes.
We present a comprehensive theory of homogeneous volatility (and variance) estimators of arbitrary stochastic processes that fully exploit the OHLC (open, high, low, close) prices. For this, we develop the theory of most efficient point-wise homogeneous OHLC volatility estimators, valid for any price processes. We intr…
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.
Proves existence of solutions to stochastic heat equations on manifolds.
problem Existence of solutions to stochastic heat equations on Riemannian manifolds.
method Proved existence using Dirichlet forms and Wiener measure.
result Established log-Sobolev inequality for the Dirichlet form in the path space.
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 …
We show that the jumps correlation matrix of a multivariate Hawkes process is related to the Hawkes kernel matrix through a system of Wiener-Hopf integral equations. A Wiener-Hopf argument allows one to prove that this system (in which the kernel matrix is the unknown) possesses a unique causal solution and consequentl…
Gaussian processes (GPs) are versatile tools that have been successfully employed to solve nonlinear estimation problems in machine learning, but that are rarely used in signal processing. In this tutorial, we present GPs for regression as a natural nonlinear extension to optimal Wiener filtering. After establishing th…
In this paper we compare two classical one-factor diffusion models which are used to model the term structure of interest rates. One of them is based on the Wiener-Bachelier process while the second one is based on the Ornstein-Uhlenbeck process. We show essential differences between the prices of European call options…
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.
The completeness problem of the bond market model with the random factors determined by a Wiener process and Poisson random measure is studied. Hedging portfolios use bonds with maturities in a countable, dense subset of a finite time interval. It is shown that under natural assumptions the market is not complete unles…
Algorithm reconstructs interaction topology in linear dynamical systems.
problem Learning influence pathways in dynamically related processes.
method Physics-informed multivariate Wiener filtering.
result Topology of interactions can be exactly recovered for certain classes.
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.
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.