Related papers: Robustness in the Optimization of Risk Measures
In this paper, we provide extended convolution bounds for the Fr\'{e}chet problem and discuss related implications in quantitative risk management. First, we establish a new form of inequality for the Range-Value-at-Risk (RVaR). Based on…
In robust optimization, the general aim is to find a solution that performs well over a set of possible parameter outcomes, the so-called uncertainty set. In this paper, we assume that the uncertainty size is not fixed, and instead aim at…
It is well known that Expected Shortfall (also called Average Value-at-Risk) is a convex risk measure, i. e. Expected Shortfall of a convex linear combination of arbitrary risk positions is not greater than a convex linear combination with…
Stochastic optimization has found wide applications in minimizing objective functions in machine learning, which motivates a lot of theoretical studies to understand its practical success. Most of existing studies focus on the convergence…
The inf-convolution of risk measures is directly related to risk sharing and general equilibrium, and it has attracted considerable attention in mathematical finance and insurance problems. However, the theory is restricted to finite sets…
In the presence of model risk, it is well-established to replace classical expected values by worst-case expectations over all models within a fixed radius from a given reference model. This is the "robustness" approach. We show that…
Resiliency has garnered attention in the management of critical infrastructure as a metric of system performance, but there are significant roadblocks to its implementation in a realistic decision-making framework. Contrasted to risk and…
We consider the portfolio optimization with risk measured by conditional value-at-risk, based on the stress event of chosen asset being equal to the opposite of its value-at-risk level, under the normality assumption. Solvability conditions…
We consider regularized support vector machines (SVMs) and show that they are precisely equivalent to a new robust optimization formulation. We show that this equivalence of robust optimization and regularization has implications for both…
This paper deals with shape optimization for elastic materials under stochastic loads. It transfers the paradigm of stochastic dominance, which allows for flexible risk aversion via comparison with benchmark random variables, from…
The robustness of risk measures to changes in underlying loss distributions (distributional uncertainty) is of crucial importance in making well-informed decisions. In this paper, we quantify, for the class of distortion risk measures with…
One major obstacle that precludes the success of reinforcement learning in real-world applications is the lack of robustness, either to model uncertainties or external disturbances, of the trained policies. Robustness is critical when the…
Financial institutions have to allocate so-called "economic capital" in order to guarantee solvency to their clients and counter parties. Mathematically speaking, any methodology of allocating capital is a "risk measure", i.e. a function…
Robustness is of central importance in machine learning and has given rise to the fields of domain generalization and invariant learning, which are concerned with improving performance on a test distribution distinct from but related to the…
The celebrated Expected Shortfall (ES) optimization formula implies that ES at a fixed probability level is the minimum of a linear real function plus a scaled mean excess function. We establish a reverse ES optimization formula, which says…
The contour maps of the error of historical resp. parametric estimates for large random portfolios optimized under the risk measure Expected Shortfall (ES) are constructed. Similar maps for the sensitivity of the portfolio weights to small…
Quantification of risk positions under model uncertainty is of crucial importance from both viewpoints of external regulation and internal management. The concept of model uncertainty, sometimes also referred to as model ambiguity. Although…
The ability to make optimal decisions under uncertainty remains important across a variety of disciplines from portfolio management to power engineering. This generally implies applying some safety margins on uncertain parameters that may…
Optimization of distortion riskmetrics with distributional uncertainty has wide applications in finance and operations research. Distortion riskmetrics include many commonly applied risk measures and deviation measures, which are not…
Quantum resource theories (QRTs) provide a unified framework to analyze quantum properties as resources for achieving advantages in quantum information processing. The generalized robustness and the weight of resource have been gaining…