Related papers: Quantiles under ambiguity and risk sharing
Causality is a central concept in a wide range of research areas, yet there is still no universally agreed axiomatisation of causality. We view causality both as an extension of probability theory and as a study of \textit{what happens when…
We provide a test for the specification of a structural model without identifying assumptions. We show the equivalence of several natural formulations of correct specification, which we take as our null hypothesis. From a natural empirical…
We generalize the AIXI reinforcement learning agent to admit a wider class of utility functions. Assigning a utility to each possible interaction history forces us to confront the ambiguity that some hypotheses in the agent's belief…
When dealing with real-world optimization problems, decision-makers usually face high levels of uncertainty associated with partial information, unknown parameters, or complex relationships between these and the problem decision variables.…
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 investigate notions of ambiguity and partial information in categorical distributional models of natural language. Probabilistic ambiguity has previously been studied using Selinger's CPM construction. This construction works well for…
We study the fundamental problem of sequential probability assignment, also known as online learning with logarithmic loss, with respect to an arbitrary, possibly nonparametric hypothesis class. Our goal is to obtain a complexity measure…
Autonomous and semi-autonomous systems are using deep learning models to improve decision-making. However, deep classifiers can be overly confident in their incorrect predictions, a major issue especially in safety-critical domains. The…
Quantile is a popular performance measure for a stochastic system to evaluate its variability and risk. To reduce the risk, selecting the actions that minimize the tail quantiles of some loss distributions is typically of interest for…
Expected Shortfall (ES), also known as superquantile or Conditional Value-at-Risk, has been recognized as an important measure in risk analysis and stochastic optimization, and is also finding applications beyond these areas. In finance, it…
In this paper we develop a novel methodology for estimation of risk capital allocation. The methodology is rooted in the theory of risk measures. We work within a general, but tractable class of law-invariant coherent risk measures, with a…
We propose a novel class of convex risk measures, based on the concept of the Fr\'echet mean, designed in order to handle uncertainty which arises from multiple information sources regarding the risk factors of interest. The proposed risk…
Risk measures satisfying the axiom of comonotonic additivity are extensively studied, arguably because of the plethora of results indicating interesting aspects of such risk measures. Recent research, however, has shown that this axiom is…
We show how risk measures originally defined in a model free framework in terms of acceptance sets and reference assets imply a meaningful underlying probability structure. Hereafter we construct a maximal domain of definition of the risk…
Expected Shortfall (ES) has been widely accepted as a risk measure that is conceptually superior to Value-at-Risk (VaR). At the same time, however, it has been criticised for issues relating to backtesting. In particular, ES has been found…
Uncertainty quantification has received increasing attention in machine learning in the recent past. In particular, a distinction between aleatoric and epistemic uncertainty has been found useful in this regard. The latter refers to the…
Our primary aim is to find an estimate of the expected shortfall in various situations: (1) Nonparametric situation, when the probability distribution of the incurred loss is unknown, only satisfying some general conditions. Then, following…
Aggregation sets, which represent model uncertainty due to unknown dependence, are an important object in the study of robust risk aggregation. In this paper, we investigate ordering relations between two aggregation sets for which the sets…
The integral representation of Choquet operators defined on a space C(X) is established by using the Choquet-Bochner integral of a real-valued function with respect to a vector capacity.
Adopting the framework of the Jaynes-Cummings model with an external quantum field, we obtain exact analytical expressions of the normally ordered moments for any kind of cavity and driving fields. Such analytical results are expressed in…