Related papers: Monetary Risk Measures
We consider learning methods based on the regularization of a convex empirical risk by a squared Hilbertian norm, a setting that includes linear predictors and non-linear predictors through positive-definite kernels. In order to go beyond…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
We provide a new characterization of second-order stochastic dominance, also known as increasing concave order. The result has an intuitive interpretation that adding a risk with negative expected value in adverse scenarios makes the…
Necessary and sufficient conditions for weak and vague convergence of measures are important for a diverse host of applications. This paper aims to give a comprehensive description of the relationship between the two modes of convergence…
We propose a robust risk measurement approach that minimizes the expectation of overestimation plus underestimation costs. We consider uncertainty by taking the supremum over a collection of probability measures, relating our approach to…
Expected Shortfall (ES) has been widely accepted as a risk measure that is conceptually superior to Value-at-Risk (VaR). At the same time, however, it has been criticised for issues relating to backtesting. In particular, ES has been found…
We present a numerically efficient approach for learning a risk-neutral measure for paths of simulated spot and option prices up to a finite horizon under convex transaction costs and convex trading constraints. This approach can then be…
Volatility is the canonical measure of financial risk, a role largely inherited from Modern Portfolio Theory. Yet, its universality rests on restrictive efficiency assumptions that render volatility, at best, an incomplete proxy for true…
Risk measure forecast and model have been developed in order to not only provide better forecast but also preserve its (empirical) property especially coherent property. Whilst the widely used risk measure of Value-at-Risk (VaR) has shown…
We consider a collection of derivatives that depend on the price of an underlying asset at expiration or maturity. The absence of arbitrage is equivalent to the existence of a risk-neutral probability distribution on the price; in…
The stability of a complex financial system may be assessed by measuring risk contagion between various financial institutions with relatively high exposure. We consider a financial network model using a bipartite graph of financial…
Empirical risk minimization (ERM) stability is usually studied via single-valued outputs, while convex non-strict losses yield set-valued minimizers. We identify Painlev\'e-Kuratowski upper semicontinuity (PK-u.s.c.) as the intrinsic…
In hedge funds, convex compensation schemes are adopted to stimulate a high-profit performance for portfolio managers. In economics, non-monotone risk aversion is proposed to argue that individuals may not be risk-averse when the wealth…
We establish strong duality relations for functional two-step compositional risk-constrained learning problems with multiple nonconvex loss functions and/or learning constraints, regardless of nonconvexity and under a minimal set of…
We propose the Star-Shaped deviation measures in the same vein as Star-Shaped risk measures and Star-Shaped acceptability indexes. We characterize Star-Shaped deviation measures through Star-Shaped acceptance sets and as the minimum of a…
In this paper we present a theoretical framework for studying coherent acceptability indices in a dynamic setup. We study dynamic coherent acceptability indices and dynamic coherent risk measures, and we establish a duality between them. We…
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 applies risk analysis to medical problems, through the properties of nonlinear responses (convex or concave). It shows 1) necessary relations between the nonlinearity of dose-response and the statistical properties of the…
In this paper, by proposing two new kinds of distributional uncertainty sets, we explore robustness of distortion risk measures against distributional uncertainty. To be precise, we first consider a distributional uncertainty set which is…
The present paper provides a representation result for monetary risk measures (i.e., monotone translation invariant functionals) satisfying a weak maxitivity property. This result can be understood as a functional analytic generalization of…