arXiv research

Hyperbolic volume correlates with chemical properties of fullerenes.

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

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…

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…

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.

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

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

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 examines Wiener process for LID estimation methods.

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.

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…

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

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

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

New linear denoiser outperforms standard Wiener filter in noisy data.

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…

New method distinguishes data noise from GP uncertainty.

A new error bound improves safety in Bayesian optimization.

Paper proposes a new model for better engine control.

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…

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…

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…

Develops trinomial models using cubature methods for financial derivative pricing.

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

The problem of image restoration in cryo-EM entails correcting for the effects of the Contrast Transfer Function (CTF) and noise. Popular methods for image restoration include `phase flipping', which corrects only for the Fourier phases but not amplitudes, and Wiener filtering, which requires the spectral signal to noi…

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 …

This paper presents a numerical model to solve the problem of cash accumulation strategies for products with an unknown future price, like assets. Stock prices are modeled by a discretized Wiener Process, and by the means of ordinary integrals this Wiener Process will be exactly matched at a preset terminal time. Three…

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…

New method estimates SDE parameters efficiently using WCE and SGD.

Model reduction methods aim to describe complex dynamic phenomena using only relevant dynamical variables, decreasing computational cost, and potentially highlighting key dynamical mechanisms. In the absence of special dynamical features such as scale separation or symmetries, the time evolution of these variables typi…

Proposes a model for identifying edges in low-rank dynamical networks.

In this we paper we recast the Cox--Ingersoll--Ross model of interest rates into the chaotic representation recently introduced by Hughston and Rafailidis. Beginning with the ``squared Gaussian representation'' of the CIR model, we find a simple expression for the fundamental random variable X. By use of techniques fro…

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

Optimal smooth subspaces approximate large data sets efficiently.

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

Construct minimal Lagrangian surfaces in complex projective plane via loop group method.

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…

In the setting proposed by Hughston & Rafailidis (2005) we consider general interest rate models in the case of a Brownian market information filtration $(\mathcal{F}_t)_{t\geq0}$. Let $X$ be a square-integrable $\mathcal{F}_\infty$-measurable random variable, and assume the non-degeneracy condition that for all $t<\in…

Study on stochastic covariant derivatives in curved space-time.

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.

New pricing methods for $α$-quantile and early-exercise options using Spitzer identities.