arXiv research

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…

Develops trinomial models using cubature methods for financial derivative pricing.

Paper develops a high-order recombination algorithm for financial modeling.

The study characterizes kernel spaces on hyperspheres, impacting cubature algorithms.

Paper introduces cubature method for stochastic Volterra equations.

New filters improve radar target inference in complex scenarios.

We study discretizations of polynomial processes using finite state Markov processes satisfying suitable moment matching conditions. The states of these Markov processes together with their transition probabilities can be interpreted as Markov cubature rules. The polynomial property allows us to study such rules using …

Algorithm finds best Dirac mass approximation of target measure.

Cubature methods, a powerful alternative to Monte Carlo due to Kusuoka~[Adv.~Math.~Econ.~6, 69--83, 2004] and Lyons--Victoir~[Proc.~R.~Soc.\\Lond.~Ser.~A 460, 169--198, 2004], involve the solution to numerous auxiliary ordinary differential equations. With focus on the Ninomiya-Victoir algorithm~[Appl.~Math.~Fin.~15, 1…

Constructs non-asymptotic confidence regions for unknown functions in RKHS.

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.

This paper gives a rigorous interpretation of a Feynman path integral on a Riemannian manifold M with non-positive sectional curvature. A $L^2$ Riemannian metric $G_P$ is given on the space of piecewise geodesic paths $H_P(M)$ adapted to the partition $P$ of $[0,1]$, whence a finite-dimensional approximation of Wiener …

The paper proves a convergence theorem for Wiener measures on holonomy groups.

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…

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 …

The paper ensures positivity of solutions to stochastic equations with positive initial data.

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…

The paper creates nonparametric confidence bands for band-limited functions.

We prove several versions of Driver's integration by parts formula for the horizontal Wiener measure on a totally geodesic Riemannian foliation and prove that the horizontal Wiener measure has a quasi-invariance property with respect to flows generated by suitable tangent processes.

Neural networks solve SPDEs using Wiener chaos expansion.

Study on stochastic covariant derivatives in curved space-time.

The paper models asset prices using Wiener chaos expansions for efficient calibration to implied volatility surfaces.

Let $W_i=\{W_i(t_i), t_i\in \R_+\}, i=1,2,\ldots,d$ are independent Wiener processes. $W=\{W(\mathbf{t}),t\in \R_+^d\}$ be the additive Wiener field define as the sum of $W_i$. 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…

New method distinguishes data noise from GP uncertainty.

New methods for $Z$-transform inversion and Wiener-Hopf factorization.

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 …

Optimal smooth subspaces approximate large data sets efficiently.

The paper examines Wiener process for LID estimation methods.

Fast method developed for pricing barrier options and joint Lévy process distributions.

In this survey article, we review the relation between heat kernels and path integrals. In particular, we review recent results on the approximation of the Wiener measure on compact manifold by measures on (finite-dimensional) spaces of piece-wise geodesics.

This paper proposes a new method to optimize portfolio allocation with transaction costs using Wiener chaos expansion.

The paper explores Wiener-Granger causality and its computational enhancements.

We present a general probabilistic perspective on Gaussian filtering and smoothing. This allows us to show that common approaches to Gaussian filtering/smoothing can be distinguished solely by their methods of computing/approximating the means and covariances of joint probabilities. This implies that novel filters and …

This work explores functional expansions to handle path dependence in various fields.

New linear denoiser outperforms standard Wiener filter in noisy data.

Dual Bayesian Affine Estimators for Wiener-type state-space models

In this work, we propose a new policy iteration algorithm for pricing Bermudan options when the payoff process cannot be written as a function of a lifted Markov process. Our approach is based on a modification of the well-known Longstaff Schwartz algorithm, in which we basically replace the standard least square regre…

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.

Paper develops a finite dimensional approximation scheme for Riemannian manifolds.

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…

A new error bound improves safety in Bayesian optimization.

We develop a technique based on Malliavin-Bismut calculus ideas, for asymptotic expansion of dual control problems arising in connection with exponential indifference valuation of claims, and with minimisation of relative entropy, in incomplete markets. The problems involve optimisation of a functional of Brownian path…

Paper proposes a new model for better engine control.

The paper improves nonparametric confidence bands for band-limited functions.

Abstract: Generalizes SGMs to infinite-dimensional Hilbertian setting.

This paper presents a new methodology to compute first-order Greeks for barrier options under the framework of path-dependent payoff functions with European, Lookback, or Asian type and with time-dependent trigger levels. In particular, we develop chain rules for Wiener path integrals between two curves that arise in t…

Hyperbolic volume correlates with chemical properties of fullerenes.