Related papers: Set risk measures
We study dynamic risk measures in a very general framework enabling to model uncertainty and processes with jumps. We previously showed the existence of a canonical equivalence class of probability measures hidden behind a given set of…
Monitoring means to observe a system for any changes which may occur over time, using a monitor or measuring device of some sort. In this paper we formulate a problem of monitoring dates of maximal risk of a financial position. Thus, the…
We propose a new ensemble prediction method, Random Subset Averaging (RSA), tailored for settings with many covariates, particularly in the presence of strong correlations. RSA constructs candidate models via binomial random subset strategy…
Much of statistics relies upon four key elements: a law of large numbers, a calculus to operationalize stochastic convergence, a central limit theorem, and a framework for constructing local approximations. These elements are…
We present a general framework for a comparative theory of variability measures, with a particular focus on the recently introduced one-parameter families of inter-Expected Shortfall differences and inter-expectile differences, that are…
We introduce the concept of partial law invariance, generalizing the concepts of law invariance and probabilistic sophistication widely used in decision theory, as well as statistical and financial applications. This new concept is…
In this paper, we propose the multivariate range Value-at-Risk (MRVaR) and the multivariate range covariance (MRCov) as two risk measures and explore their desirable properties in risk management. In particular, we explain that such…
In this paper, we develop a unified framework for studying constrained robust optimal control problems with adjustable uncertainty sets. In contrast to standard constrained robust optimal control problems with known uncertainty sets, we…
We introduce a new measure of performance of investment strategies, the monotone Sharpe ratio. We study its properties, establish a connection with coherent risk measures, and obtain an efficient representation for using in applications.
Risk management often plays an important role in decision making under uncertainty. In quantitative risk management, assessing and optimizing risk metrics requires efficient computing techniques and reliable theoretical guarantees. In this…
The theory of convex risk functions has now been well established as the basis for identifying the families of risk functions that should be used in risk averse optimization problems. Despite its theoretical appeal, the implementation of a…
Compressive sensing (CS) is well-known for its unique functionalities of sensing, compressing, and security (i.e. CS measurements are equally important). However, there is a tradeoff. Improving sensing and compressing efficiency with prior…
We derive bounds on the sample complexity of empirical risk minimization (ERM) in the context of minimizing non-convex risks that admit the strict saddle property. Recent progress in non-convex optimization has yielded efficient algorithms…
Recently, invariant risk minimization (IRM) was proposed as a promising solution to address out-of-distribution (OOD) generalization. However, it is unclear when IRM should be preferred over the widely-employed empirical risk minimization…
Many uncertainty sets encountered in control systems analysis and design can be expressed in terms of semialgebraic sets, that is as the intersection of sets described by means of polynomial inequalities. Important examples are for instance…
In this paper, we introduce two alternative extensions of the classical univariate Value-at-Risk (VaR) in a multivariate setting. The two proposed multivariate VaR are vector-valued measures with the same dimension as the underlying risk…
Despite decades of research in risk management, most of the literature has focused on scalar risk measures (like e.g. Value-at-Risk and Expected Shortfall). While such scalar measures provide compact and tractable summaries, they provide a…
We study statistical properties of the optimal value and optimal solutions of the Sample Average Approximation of risk averse stochastic problems. Central Limit Theorem type results are derived for the optimal value and optimal solutions…
In this paper, we consider a multi-objective control problem for stochastic systems that seeks to minimize a cost of interest while ensuring safety. We introduce a novel measure of safety risk using the conditional value-at-risk and a set…
Motivated by recent work on monotone additive statistics and questions regarding optimal risk sharing for return-based risk measures, we investigate the existence, structure, and applications of Meyer risk measures. Those are monetary risk…