Related papers: Elicitability of Return Risk Measures
Optimization of conditional convex risk measure is a central theme in dynamic portfolio selection theory, which has not yet systematically studied in the previous literature perhaps since conditional convex risk measures are neither random…
Given an Orlicz function $M$, we show which random variables $\xi_i$, $i=1,...,n$ generate the associated Orlicz norm, i.e., which random variables yield $\mathbb{E} \max\limits_{1\leq i \leq n}|x_i\xi_i| \sim \norm{(x_i)_{i=1}^n}_M$. As a…
Under appropriate integrability conditions the risk measure of the sample measures for a law invariant risk measure converge almost surely to the risk measure of the sampled random variable. The results follow from general convergence…
This paper introduces and fully characterizes the novel class of quasi-logconvex measures of risk, to stand on equal footing with the rich class of quasi-convex measures of risk. Quasi-logconvex risk measures naturally generalize logconvex…
We consider different types of predictive intervals and ask whether they are elicitable, i.e. are unique minimizers of a loss or scoring function in expectation. The equal-tailed interval is elicitable, with a rich class of suitable loss…
In this paper, we study general monetary risk measures (without any convexity or weak convexity). A monetary (respectively, positively homogeneous) risk measure can be characterized as the lower envelope of a family of convex (respectively,…
Systemic risk measures such as CoVaR, CoES and MES are widely-used in finance, macroeconomics and by regulatory bodies. Despite their importance, we show that they fail to be elicitable and identifiable. This renders forecast comparison and…
Recent advances in multi-task peer prediction have greatly expanded our knowledge about the power of multi-task peer prediction mechanisms. Various mechanisms have been proposed in different settings to elicit different types of…
This paper is devoted to the introduction and study of a new family of multivariate elicitable risk measures. We call the obtained vector-valued measures multivariate expectiles. We present the different approaches used to construct our…
In this paper we introduce a generalization of classical risk measures in which the risk is represented by a step function taking two values, corresponding to two endogenously determined market regimes. This extends the traditional…
In this research, starting from a widely accepted definition of risk, we support the idea that risk reduction is a more realistic objective than risk minimization, which represents a theoretical utopia. Furthermore, significant risk…
In this paper we study the differentially private Empirical Risk Minimization (ERM) problem in different settings. For smooth (strongly) convex loss function with or without (non)-smooth regularization, we give algorithms that achieve…
We prove uniform estimates for the expected value of averages of order statistics of bivariate functions in terms of their largest values by a direct analysis. As an application, uniform estimates for the expected value of averages of order…
This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general…
We revisit the recently introduced concept of return risk measures (RRMs) and extend it by incorporating risk management via multiple so-called eligible assets. The resulting new class of risk measures, termed multi-asset return risk…
In this paper, we study properties of certain risk measures associated with acceptance sets. These sets describe regulatory preconditions that have to be fulfilled by financial institutions to pass a given acceptance test. If the financial…
In the face of uncertainty, the need for probabilistic assessments has long been recognized in the literature on forecasting. In classification, however, comparative evaluation of classifiers often focuses on predictions specifying a single…
In this short note, we show that every convex, order bounded above functional on a Frechet lattice is automatically norm continuous. This improves a result in \cite{RS06} and applies to many deviation and variability measures. We also show…
Environmental variables that fluctuate randomly and dynamically over time, such as water quality indices, are considered to be stochastic. They exhibit sub-exponential memory structures that should be accounted for in their modeling and…
An analyst is tasked with producing a statistical study. The analyst is not monitored and is able to manipulate the study. He can receive payments contingent on his report and trusted data collected from an independent source, modeled as a…