Related papers: Set risk measures
We give both sufficient conditions and necessary conditions for the stochastic stability of non-uniformly expanding maps either with or without critical sets. We also show that the number of probability measures describing the statistical…
We propose a generalization of the classical notion of the $V@R_{\lambda}$ that takes into account not only the probability of the losses, but the balance between such probability and the amount of the loss. This is obtained by defining a…
The time value of money is a critical factor not only in risk analysis, but also in insurance and financial applications. In this paper, we consider a special class of set-valued risk statistics by introducing the time value of money. In…
We propose a new approach, termed Realized Risk Measures (RRM), to estimate Value-at-Risk (VaR) and Expected Shortfall (ES) using high-frequency financial data. It extends the Realized Quantile (RQ) approach proposed by Dimitriadis and…
Empirical risk minimization can lead to poor generalization behavior on unseen environments if the learned model does not capture invariant feature representations. Invariant risk minimization (IRM) is a recent proposal for discovering…
Risk-sensitive planning aims to identify policies maximizing some tail-focused metrics in Markov Decision Processes (MDPs). Such an optimization task can be very costly for the most widely used and interpretable metrics such as threshold…
Starting from the requirement that risk measures of financial portfolios should be based on their losses, not their gains, we define the notion of loss-based risk measure and study the properties of this class of risk measures. We…
A risk analyst assesses potential financial losses based on multiple sources of information. Often, the assessment does not only depend on the specification of the loss random variable but also various economic scenarios. Motivated by this…
We establish a profound connection between coherent risk measures, a prominent object in quantitative finance, and uniform integrability, a fundamental concept in probability theory. Instead of working with absolute values of random…
In this paper, we discuss various problems in the usage and definition of risk matrices. We give an overview of the general process of risk assessment with risk matrices and ordinal scales. Furthermore, we explain the fallacies in each…
The financial crisis showed the importance of measuring, allocating and regulating systemic risk. Recently, the systemic risk measures that can be decomposed into an aggregation function and a scalar measure of risk, received a lot of…
Evaluation of systemic risk in networks of financial institutions in general requires information of inter-institution financial exposures. In the framework of Debt Rank algorithm, we introduce an approximate method of systemic risk…
Signomial programs (SPs) are optimization problems specified in terms of signomials, which are weighted sums of exponentials composed with linear functionals of a decision variable. SPs are non-convex optimization problems in general, and…
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…
This paper gives an overview of the theory of dynamic convex risk measures for random variables in discrete time setting. We summarize robust representation results of conditional convex risk measures, and we characterize various time…
In this paper monetary risk measures that are positively superhomogeneous, called star-shaped risk measures, are characterized and their properties studied. The measures in this class, which arise when the controversial subadditivity…
In this paper, we study convex risk measures with weak optimal transport penalties. In a first step, we show that these risk measures allow for an explicit representation via a nonlinear transform of the loss function. In a second step, we…
The empirical risk minimization (ERM) problem with relative entropy regularization (ERM-RER) is investigated under the assumption that the reference measure is a $\sigma$-finite measure, and not necessarily a probability measure. Under this…
This paper investigates systemic risk measures for stochastic financial networks of explicitly modelled bilateral liabilities. We extend the notion of systemic risk measures from Biagini, Fouque, Fritelli and Meyer-Brandis (2019) to graph…
Sequential monitoring of randomized trials traditionally relies on parametric assumptions or asymptotic approximations. We discuss a family of nonparametric sequential tests - collectively called e-RT - for binary, event-only, and…