Related papers: Multivariate transient price impact and matrix-val…

We propose a greedy strategy to spectrally train a deep network for multi-class classification. Each layer is defined as a composition of linear weights with the feature map of a Gaussian kernel acting as the activation function. At each…

In this article we consider the Merton problem in a market with a single risky asset and transaction costs. We give a complete solution of the problem up to the solution of a free-boundary problem for a first-order differential equation,…

Dyadic data is often encountered when quantities of interest are associated with the edges of a network. As such it plays an important role in statistics, econometrics and many other data science disciplines. We consider the problem of…

Robust stability problem of integral delay systems with uncertain kernel matrix functions is addressed in this paper. On the basis of characteristic equation and the argument principle, an algorithm is generated which is shown to outperform…

If a real-valued function is continuous on a real interval and it takes on two different values, then it will also take any value in between those two, by the Intermediate Value Theorem. It is not immediately clear what would be a natural…

The constitutive modelling of granular, porous and quasi-brittle materials is based on yield (or damage) functions, which may exhibit features (for instance, lack of convexity, or branches where the values go to infinity, or false elastic…

Regression tasks, notably in safety-critical domains, require proper uncertainty quantification, yet the literature remains largely classification-focused. In this light, we introduce a family of measures for total, aleatoric, and epistemic…

The effective action of the linear meson model generates the mesonic n-point functions with all quantum effects included. Based on chiral symmetry and a systematic quark mass expansion we derive relations between meson masses and decay…

We study hedging and pricing of unattainable contingent claims in a non-Markovian regime-switching financial model. Our financial market consists of a bank account and a risky asset whose dynamics are driven by a Brownian motion and a…

Performative prediction is a framework for learning models that influence the data they intend to predict. We focus on finding classifiers that are performatively stable, i.e. optimal for the data distribution they induce. Standard…

This paper concerns the tilt stability of local optimal solutions to a class of nonlinear semidefinite programs, which involves a twice continuously differentiable objective function and a convex feasible set. By leveraging the second…

Optimization problems with discrete decisions are nonconvex and thus lack strong duality, which limits the usefulness of tools such as shadow prices and the KKT conditions. It was shown in Burer(2009) that mixed-binary quadratic programs…

In the absence of unobserved confounders, matching and weighting methods are widely used to estimate causal quantities including the Average Treatment Effect on the Treated (ATT). Unfortunately, these methods do not necessarily achieve…

Kernel matrices are crucial in many learning tasks such as support vector machines or kernel ridge regression. The kernel matrix is typically dense and large-scale. Depending on the dimension of the feature space even the computation of all…

For two continuous and isotropic positive definite kernels on the same compact two-point homogeneous space, we determine necessary and sufficient conditions in order that their product be strictly positive definite. We also provide a…

Nonlinear control systems with partial information to the decision maker are prevalent in a variety of applications. As a step toward studying such nonlinear systems, this work explores reinforcement learning methods for finding the optimal…

The simple product formulae for derivatives of scalar functions raised to different powers are generalized for functions which take values in the set of symmetric positive definite matrices. These formulae are fundamental in derivation of…

Precision matrix estimation is a cornerstone concept in statistics, economics, and finance. Despite advances in recent years, estimation methods that are simultaneously (i) dense, (ii) consistent, and (iii) model-free are lacking. While…

The numeraire portfolio in a financial market is the unique positive wealth process that makes all other nonnegative wealth processes, when deflated by it, supermartingales. The numeraire portfolio depends on market characteristics, which…

We introduce a discrete binary tree for pricing contingent claims with the underlying security prices exhibiting history dependence characteristic of that induced by market microstructure phenomena. Example dependencies considered include…