Related papers: The randomly distorted Choquet integrals with resp…
The paper investigates the robust distortion risk measure with linear penalty function under distribution uncertainty. The distribution uncertainties are characterized by predetermined moment conditions or constraints on the Wasserstein…
It is well known that a random vector with given marginal distributions is comonotonic if and only if it has the largest sum with respect to the convex order [ Kaas, Dhaene, Vyncke, Goovaerts, Denuit (2002), A simple geometric proof that…
Machine learning typically presupposes classical probability theory which implies that aggregation is built upon expectation. There are now multiple reasons to motivate looking at richer alternatives to classical probability theory as a…
Generalized equations are problems emerging in contexts of modern variational analysis as an adequate formalism to treat such issues as constraint systems, optimality and equilibrium conditions, variational inequalities, differential…
Within the context of capital adequacy, we study comonotonicity of risk measures in terms of the primitives of the theory: acceptance sets and eligible, or reference, assets. We show that comonotonicity cannot be characterized by the…
This article deals with the generalization performance of margin multi-category classifiers, when minimal learnability hypotheses are made. In that context, the derivation of a guaranteed risk is based on the handling of capacity measures…
A practical limitation of cluster randomized controlled trials (cRCTs) is that the number of available clusters may be small, resulting in an increased risk of baseline imbalance under simple randomization. Constrained randomization…
In this article we study the expanding properties of random perturbations of contracting Lorenz maps satisfying the summability condition of exponent 1. Under general conditions on the maps and perturbation types, we prove stochastic…
We introduce a novel framework to account for sensitivity to rewards uncertainty in sequential decision-making problems. While risk-sensitive formulations for Markov decision processes studied so far focus on the distribution of the…
Convexity and quasiconvexity are two properties that capture the concept of diversification for risk measures. Between the two, there is natural quasiconvexity, an old but not so well-known property weaker than convexity but stronger than…
We investigate the conditions under which the space of bounded harmonic functions of a probability measure $\mu$ on a group $G$ is contained in that of another measure $\theta$. We establish that asymptotic commutativity, defined by the…
In causal inference, estimating the average treatment effect is a central objective, and in the context of competing risks data, this effect can be quantified by the cause-specific cumulative incidence function (CIF) difference. While…
We model chaotic diffusion, in a symplectic 4D map by using the result of a theorem that was developed for stochastically perturbed integrable Hamiltonian systems. We explicitly consider a map defined by a free rotator (FR) coupled to a…
In this paper, an optimization problem with uncertain constraint coefficients is considered. Possibility theory is used to model the uncertainty. Namely, a joint possibility distribution in constraint coefficient realizations, called…
In this paper, we focus on efficient risk-sharing rules for the concave dominance order. For a univariate risk, it follows from a comonotone dominance principle, due to Landsberger and Meilijson [25], that efficiency is characterized by a…
To provide a solid analytic foundation for the module approach to conditional risk measures, this paper establishes a complete random convex analysis over random locally convex modules by simultaneously considering the two kinds of…
An effective characterization of chaotic conservative Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor derived from the structure of the Hamiltonian has been extended to a wide class of potential…
We establish a dilation-theoretic characterization of the Choquet order on the space of measures on a compact convex set using ideas from the theory of operator algebras. This yields an extension of Cartier's dilation theorem to the…
We consider the cosmology where some function f(G) of the Gauss-Bonnet term G is added to the gravitational action to account for the late-time accelerating expansion of the universe. The covariant and gauge invariant perturbation equations…
Perturbation theory of vacuum spherically-symmetric spacetimes (including the cosmological constant) has greatly contributed to the understanding of black holes, relativistic compact stars and even inhomogeneous cosmological models. The…