Related papers: On the Dual Representation of Coherent Risk Measur…
Risk measures connect probability theory or statistics to optimization, particularly to convex optimization. They are nowadays standard in applications of finance and in insurance involving risk aversion. This paper investigates a wide…
We propose a multivariate extension of a well-known characterization by S. Kusuoka of regular and coherent risk measures as maximal correlation functionals. This involves an extension of the notion of comonotonicity to random vectors…
In this paper we derive robust super- and subhedging dualities for contingent claims that can depend on several underlying assets. In addition to strict super- and subhedging, we also consider relaxed versions which, instead of eliminating…
Measuring and managing risk has become crucial in modern decision making under stochastic uncertainty. In two-stage stochastic programming, mean risk models are essentially defined by a parametric recourse problem and a quantification of…
We introduce a framework for quantifying propagation of uncertainty arising in a dynamic setting. Specifically, we define dynamic uncertainty sets designed explicitly for discrete stochastic processes over a finite time horizon. These…
By representing the range of fair betting odds according to a pair of confidence set estimators, dual probability measures on parameter space called frequentist posteriors secure the coherence of subjective inference without any prior…
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…
Monetary risk measures are usually interpreted as the smallest amount of external capital that must be added to a financial position to make it acceptable. We propose a new concept: intrinsic risk measures and argue that this approach…
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…
This survey gives an introduction to monetary measures of risk as monotone and cash additive functions on spaces of univariate random variables. Primal and dual representation results as well as several examples are discussed. Principal…
Recently, literature on dynamic coherent risk measures has broadened the choices for risk-sensitive performance evaluation. A running example includes Cumulative prospect theory and Conditional variance at risk. Most of them can be can be…
The paper investigates the robust optimized certainty equivalents and analyzes the relevant properties of them as risk measures for loss positions with distribution uncertainty. On this basis, the robust generalized quantiles are proposed…
We study strategic interaction in data-driven games where players face uncertainty about payoff distributions inferred from finite samples. To model calibrated attitudes toward such uncertainty, we formulate distributionally robust games…
We show that a wide class of risk-constrained nonconvex functional optimization problems exhibit strong duality, regardless of nonconvexity. We develop two novel results under distinct sets of assumptions, establishing strong duality over…
Motivated by the results of static monetary or star-shaped risk measures, the paper investigates the representation theorems in the dynamic framework. We show that dynamic monetary risk measures can be represented as the lower envelope of a…
We characterize when a convex risk measure associated to a law-invariant acceptance set in $L^\infty$ can be extended to $L^p$, $1\leq p<\infty$, preserving finiteness and continuity. This problem is strongly connected to the statistical…
We provide a constructive way of defining new elicitable risk measures that are characterised by a multiplicative scoring function. We show that depending on the choice of the scoring function's components, the resulting risk measure…
Different approaches to defining dynamic market risk measures are available in the literature. Most are focused or derived from probability theory, economic behavior or dynamic programming. Here, we propose an approach to define and…
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…
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…