arXiv research

New finite element method for complex forms in any dimension.

A new discrete calculus for bundle-valued forms is proposed and validated.

An explicit formula is derived for the value of weak information in a discrete time model that works for a wide range of utility functions including the logarithmic and power utility. We assume a complete market with a finite number of assets and a finite number of possible outcomes. Explicit calculations are performed…

The paper explores heat flow and constants on graphs, proving properties and proposing new concepts.

There is a need for the development of models that are able to account for discreteness in data, along with its time series properties and correlation. Our focus falls on INteger-valued AutoRegressive (INAR) type models. The INAR type models can be used in conjunction with existing model-based clustering techniques to …

This paper addresses the morphing of manifold-valued images based on the time discrete geodesic paths model of Berkels, Effland and Rumpf 2015. Although for our manifold-valued setting such an interpretation of the energy functional is not available so far, the model is interesting on its own. We prove the existence of…

We give a general formulation of the utility maximization problem under nondominated model uncertainty in discrete time and show that an optimal portfolio exists for any utility function that is bounded from above. In the unbounded case, integrability conditions are needed as nonexistence may arise even if the value fu…

Study error bounds in evaluating distributional computational graphs.

The paper finds upper bounds for the continuous part of the axial distance spectrum for Kleinian groups.

In this article, a compact finite difference method is proposed for pricing European and American options under jump-diffusion models. Partial integro-differential equation and linear complementary problem governing European and American options respectively are discretized using Crank-Nicolson Leap-Frog scheme. In pro…

Analytic submanifolds of cocycles reveal discrete cohomology spaces.

IDF++ improves integer discrete flows for lossless compression.

The paper solves circle packings on surfaces with boundaries.

The paper defines and studies discrete p-density and compression-radius profiles of lattice knots.

New boundary treatment improves accuracy for complex PDEs.

New insights into RL efficiency from managing time discretization.

We study time-consistency questions for processes of monetary risk measures that depend on bounded discrete-time processes describing the evolution of financial values. The time horizon can be finite or infinite. We call a process of monetary risk measures time-consistent if it assigns to a process of financial values …

Method infers causal structure from system behaviors using RKHS and kernel $ε$-machines.

In this expository paper we illustrate the generality of game theoretic probability protocols of Shafer and Vovk (2001) in finite-horizon discrete games. By restricting ourselves to finite-horizon discrete games, we can explicitly describe how discrete distributions with finite support and the discrete pricing formulas…

New discrete-time model shows insider trading dynamics.

We prove a general duality result for multi-stage portfolio optimization problems in markets with proportional transaction costs. The financial market is described by Kabanov's model of foreign exchange markets over a finite probability space and finite-horizon discrete time steps. This framework allows us to compare v…

The study examines discrete subgroups of Lie groups and their residual finiteness.

We prove that any connected component of the space of m-spin structures on compact Riemann surfaces with finite number of punctures and holes is homeomorphic to a quotient of the vector space R^d by a discrete group action. Our proof is based on the representation of the space of m-spin structures on a Riemann surface …

Study stability of contingent claim solutions under probabilistic perturbations.

A Neural Network (NN) based numerical method is formulated and implemented for solving Boundary Value Problems (BVPs) and numerical results are presented to validate this method by solving Laplace equation with Dirichlet boundary condition and Poisson's equation with mixed boundary conditions. The principal advantage o…

The aim of this paper is to find an optimal matching between manifold-valued curves, and thereby adequately compare their shapes, seen as equivalent classes with respect to the action of reparameterization. Using a canonical decomposition of a path in a principal bundle, we introduce a simple algorithm that finds an op…

Discrete Gaussian noise preserves privacy and accuracy in differential privacy.

Study shows financial value of weak information converges in discrete vs continuous markets.

New method for mesh denoising using TGV of normal vector field.

We apply a utility-based method to obtain the value of a finite-time investment opportunity when the underlying real asset is not perfectly correlated to a traded financial asset. Using a discrete-time algorithm to calculate the indifference price for this type of real option, we present numerical examples for the corr…

Study finite-energy metrics over complex manifold degenerations.

Simulated annealing is a popular method for approaching the solution of a global optimization problem. Existing results on its performance apply to discrete combinatorial optimization where the optimization variables can assume only a finite set of possible values. We introduce a new general formulation of simulated an…

We define for arbitrary modules over a finite von Neumann algebra $\cala$ a dimension taking values in $[0,\infty]$ which extends the classical notion of von Neumann dimension for finitely generated projective $\cala$-modules and inherits all its useful properties such as additivity, cofinality and continuity. This all…

The paper constructs discrete Hessian and divdiv complexes on triangulations and proves their cohomology isomorphic to continuous versions.

CoNNTrA trains DNNs with low-power, low-memory constraints.

This paper demonstrates a practical method for computing the solution of an expectation-constrained robust maximization problem with immediate applications to model-free no-arbitrage bounds and super-replication values for many financial derivatives. While the previous literature has connected super-replication values …

Graphically discrete groups have strong rigidity properties.

We construct an infinite discrete subgroup of the isometry group of $\mathbb H^3$ with no finite quotients other than the trivial group.

Factorizes discrete representations of finitely generated groups into PSL(2, R).

A new method for anomaly detection adapts to local non-stationarity in low-data regimes.

Paper proves a discrete Schwarz-Pick lemma for generalized circle packings.

Study identifies and analyzes three types of errors in learning Fourier operators.

We develop methods to efficiently approximate data in metric spaces without additional assumptions.

Study on 2-valued dynamics on complex plane, showing some dynamics can't be group actions.

No stable discrete maps into certain curved spaces exist.

Estimating causal models from observational data is a crucial task in data analysis. For continuous-valued data, Shimizu et al. have proposed a linear acyclic non-Gaussian model to understand the data generating process, and have shown that their model is identifiable when the number of data is sufficiently large. Howe…

Recurrent neural networks (RNNs) are an effective representation of control policies for a wide range of reinforcement and imitation learning problems. RNN policies, however, are particularly difficult to explain, understand, and analyze due to their use of continuous-valued memory vectors and observation features. In …

Let $M$ be an open Riemann surface and $n\ge 3$ be an integer. We prove that on any closed discrete subset of $M$ one can prescribe the values of a conformal minimal immersion $M\to\mathbb{R}^n$. Our result also ensures jet-interpolation of given finite order, and hence, in particular, one may in addition prescribe the…