Related papers: Set-valued Star-Shaped Risk Measures
This paper is mainly a survey of recent research developments regarding methods for risk minimization in financial markets modeled by It\^o-L\'evy processes, but it also contains some new results on the underlying stochastic maximum…
In this note we consider a system of financial institutions and study systemic risk measures in the presence of a financial market and in a robust setting, namely, where no reference probability is assigned. We obtain a dual representation…
Credit ratings are widely used by investors as a screening device. We introduce and study several natural notions of risk consistency that promote prudent investment decisions in the framework of Choquet rating criteria. Three closely…
In this article we propose a novel measure of systemic risk in the context of financial networks. To this aim, we provide a definition of systemic risk which is based on the structure, developed at different levels, of clustered neighbours…
We extend the scope of risk measures for which backtesting models are available by proposing a multinomial backtesting method for general distortion risk measures. The method relies on a stratification and randomization of risk levels. We…
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 article, we consider models for time-to-event data obtained from experiments in which stress levels are altered at intermediate stages during the observation period. These experiments, known as step-stress tests, belong to the…
We consider risk-averse convex stochastic programs expressed in terms of extended polyhedral risk measures. We derive computable confidence intervals on the optimal value of such stochastic programs using the Robust Stochastic Approximation…
A generalization of expectiles for d-dimensional multivariate distribution functions is introduced. The resulting geometric expectiles are unique solutions to a convex risk minimization problem and are given by d-dimensional vectors. They…
We study submodularity for law-invariant functionals, with particular attention to convex risk measures. Expected losses are modular, and certainty equivalents are submodular exactly when the loss function is convex. Law-invariant coherent…
Higher order risk measures are stochastic optimization problems by design, and for this reason they enjoy valuable properties in optimization under uncertainties. They nicely integrate with stochastic optimization problems, as has been…
This paper develops a unified framework for the robustification of risk measures beyond the classical convex and cash-additive setting. We consider general risk measures on Lp spaces and construct their robust counterparts through families…
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…
In this paper, we propose a novel axiomatic approach to evaluating the joint risk of multiple insurance risks under dependence uncertainty. Motivated by both the theory of expected utility and the Cobb-Dauglas utility function, we establish…
We propose a new system identification method, called Sign-Perturbed Sums (SPS), for constructing non-asymptotic confidence regions under mild statistical assumptions. SPS is introduced for linear regression models, including but not…
In the framework of the generalized measure theory the decomposable probabilistic-valued set functions are introduced with triangle functions $\tau$ in an appropriate probabilistic metric space as natural candidates for the "addition",…
In this paper we study time-consistent risk measures for returns that are given by a GARCH(1,1) model. We present a construction of risk measures based on their static counterparts that overcomes the lack of time-consistency. We then study…
Recently, financial industry and regulators have enhanced the debate on the good properties of a risk measure. A fundamental issue is the evaluation of the quality of a risk estimation. On the one hand, a backtesting procedure is desirable…
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 develop a statistical framework for risk estimation, inspired by the axiomatic theory of risk measures. Coherent risk estimators -- functionals of P\&L samples inheriting the economic properties of risk measures -- are defined and…