Related papers: Coherent risk measures and uniform integrability

How can we draw trustworthy scientific conclusions? One criterion is that a study can be replicated by independent teams. While replication is critically important, it is arguably insufficient. If a study is biased for some reason and other…

Foster and Hart proposed an operational measure of riskiness for discrete random variables. We show that their defining equation has no solution for many common continuous distributions including many uniform distributions, e.g. We show how…

Purpose: A new point of view in the study of impact is introduced. Approach: Using fundamental theorems in real analysis we study the convergence of well-known impact measures. Findings: We show that pointwise convergence is maintained by…

Risk assessment under different possible scenarios is a source of uncertainty that may lead to concerning financial losses. We address this issue, first, by adapting a robust framework to the class of spectral risk measures. Second, we…

This paper presents uniform estimation and inference theory for a large class of nonparametric partitioning-based M-estimators. The main theoretical results include: (i) uniform consistency for convex and non-convex objective functions;…

We develop a method to generate prediction sets with a guaranteed coverage rate that is robust to corruptions in the training data, such as missing or noisy variables. Our approach builds on conformal prediction, a powerful framework to…

We discuss equivalent axiomatic characterizations of distortion risk measures, and give a novel and concise proof of the characterization of elicitable distortion risk measures. Elicitability has recently been discussed as a desirable…

Despite the versatility of generalized linear mixed models in handling complex experimental designs, they often suffer from misspecification and convergence problems. This makes inference on the values of coefficients problematic. To…

We give a complete characterization of both comonotone and not comonotone coherent risk measures in the discrete finite probability space, where each outcome is equally likely. To the best of our knowledge, this is the first work that…

Credal sets, i.e., closed convex sets of probability measures, provide a natural framework to represent aleatoric and epistemic uncertainty in machine learning. Yet how to quantify these two types of uncertainty for a given credal set,…

Reasoning with fuzzy sets can be achieved through measures such as similarity and distance. However, these measures can often give misleading results when considered independently, for example giving the same value for two different pairs…

We consider the problem of representing claims for coherent risk measures. For this purpose we introduce the concept of (weak and strong) time-consistency with respect to a portfolio of assets, generalizing the one defined by Delbaen. In a…

We propose a pricing technique based on coherent risk measures, which enables one to get finer price intervals than in the No Good Deals pricing. The main idea consists in splitting a liability into several parts and selling these parts to…

Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…

We introduce a novel measure of dependence that captures the extent to which a random variable $Y$ is determined by a random vector $X$. The measure equals zero precisely when $Y$ and $X$ are independent, and it attains one exactly when $Y$…

Testing the independence between random vectors is a fundamental problem in statistics. Distance correlation, a recently popular dependence measure, is universally consistent for testing independence against all distributions with finite…

This paper offers a mathematical invention that shows how to convert integrated quantiles, which often appear in risk measures, into integrated cumulative distribution functions, which are technically more tractable from various…

Stemming from de Finetti's work on finitely additive coherent probabilities, the paradigm of coherence has been applied to many uncertainty calculi in order to remove structural restrictions on the domain of the assessment. Three possible…

In a model with no given probability measure, we consider asset pricing in the presence of frictions and other imperfections and characterize the property of coherent pricing, a notion related to (but much weaker than) the no arbitrage…

While the traditional viewpoint in machine learning and statistics assumes training and testing samples come from the same population, practice belies this fiction. One strategy -- coming from robust statistics and optimization -- is thus…