Related papers: Non-Smooth Integrability Theory
We study the dual formulation of the utility maximization problem in incomplete markets when the utility function is finitely valued on the whole real line. We extend the existing results in this literature in two directions. First, we…
We study Neumann functions for divergence form, second order elliptic systems with bounded measurable coefficients in a bounded Lipschitz domain or a Lipschitz graph domain. We establish existence, uniqueness, and various estimates for the…
This note studies numerical methods for solving compositional optimization problems, where the inner function is smooth, and the outer function is Lipschitz continuous, non-smooth, and non-convex but exhibits one of two special structures…
Demand-side management provides a great potential for improving the efficiency and reliability of energy systems. This requires a mechanism to connect the market level and the demand side. The flexibility function is a novel approach that…
We provide sufficient conditions for a locally lipschitz mapping to be invertible . We use classical local invertibility conditions together with the non-smooth critical point theory.
We study unconstrained optimization problems of nonsmooth, nonconvex Lipschitz functions, using only noisy pairwise comparisons governed by a known link function. Our goal is to compute a $(\delta,\varepsilon)$-Goldstein stationary point.…
The problem of demand inversion - a crucial step in the estimation of random utility discrete-choice models - is equivalent to the determination of stable outcomes in two-sided matching models. This equivalence applies to random utility…
Demand forecasting is a crucial component of demand management. While shortening the forecasting horizon allows for more recent data and less uncertainty, this frequently means lower data aggregation levels and a more significant data…
We consider the problem of estimating smooth integrated functionals of a monotone nonincreasing density $f$ on $[0,\infty)$ using the nonparametric maximum likelihood based plug-in estimator. We find the exact asymptotic distribution of…
We prove two compactness results for function spaces with finite Dirichlet energy of half-space nonlocal gradients. In each of these results, we provide sufficient conditions on a sequence of kernel functions that guarantee the asymptotic…
To tackle difficulties for theoretical studies in situations involving nonsmooth functions, we propose a sequence of infinitely differentiable functions to approximate the nonsmooth function under consideration. A rate of approximation is…
We study the minimax identity for a non-decreasing upper-semicontinuous utility function satisfying mild growth assumption. In contrast to the classical setting, we do not impose the assumption that the utility function is concave. By…
We prove a compact embedding theorem in a class of spaces of piecewise H1 functions subordinated to a class of shape regular, but not necessarily quasi-uniform triangulations of a polygonal domain. This result generalizes the…
We consider a stochastic financial incomplete market where the price processes are described by a vector-valued semimartingale that is possibly nonlocally bounded. We face the classical problem of utility maximization from terminal wealth,…
We consider a functional calculus for compact operators, acting on the singular values rather than the spectrum, which appears frequently in applied mathematics. Necessary and sufficient conditions for this singular value functional…
We consider the problem of maximizing expected utility from consumption in a constrained incomplete semimartingale market with a random endowment process, and establish a general existence and uniqueness result using techniques from convex…
A compactness of the Revuz map is established in the sense that the locally uniform convergence of a sequence of positive continuous additive functionals is derived in terms of their smooth measures. To this end, we first introduce a metric…
We study properties of ridge functions $f(x)=g(a\cdot x)$ in high dimensions $d$ from the viewpoint of approximation theory. The considered function classes consist of ridge functions such that the profile $g$ is a member of a univariate…
We consider a composite optimization problem where the sum of a continuously differentiable and a merely lower semicontinuous function has to be minimized. The proximal gradient algorithm is the classical method for solving such a problem…
We apply the topology of convergence on compact sets to define unpredictable functions [5, 6]. The topology is metrizable and easy for applications with integral operators. To demonstrate the effectiveness of the approach, the existence and…