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The ongoing concern about systemic risk since the outburst of the global financial crisis has highlighted the need for risk measures at the level of sets of interconnected financial components, such as portfolios, institutions or members of…
When estimating the risk of a P&L from historical data or Monte Carlo simulation, the robustness of the estimate is important. We argue here that Hampel's classical notion of qualitative robustness is not suitable for risk measurement and…
We offer a new perspective on risk aggregation with FGM copulas. Along the way, we discover new results and revisit existing ones, providing simpler formulas than one can find in the existing literature. This paper builds on two novel…
Regularized empirical risk minimization with constrained labels (in contrast to fixed labels) is a remarkably general abstraction of learning. For common loss and regularization functions, this optimization problem assumes the form of a…
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…
We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a…
Consider an insurance company exposed to a stochastic economic environment that contains two kinds of risk. The first kind is the insurance risk caused by traditional insurance claims, and the second kind is the financial risk resulting…
Most high-dimensional estimation and prediction methods propose to minimize a cost function (empirical risk) that is written as a sum of losses associated to each data point. In this paper we focus on the case of non-convex losses, which is…
Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave…
We develop a method for computing policies in Markov decision processes with risk-sensitive measures subject to temporal logic constraints. Specifically, we use a particular risk-sensitive measure from cumulative prospect theory, which has…
Since the quasiconvex risk measures is a bigger class than the well known convex risk measures, the study of quasiconvex risk measures makes sense especially in the financial markets with volatility. In this paper, we will study the…
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…
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…
Classes of multivariate and cone valued infinitely divisible Gamma distributions are introduced. Particular emphasis is put on the cone-valued case, due to the relevance of infinitely divisible distributions on the positive semi-definite…
This paper presents a systematic study of the notion of surplus invariance, which plays a natural and important role in the theory of risk measures and capital requirements. So far, this notion has been investigated in the setting of some…
Building on recent results regarding symmetric probabilistic constructions of countable structures, we provide a method for constructing probability measures, concentrated on certain classes of countably infinite structures, that are…
Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these…
There is wide interest in studying how the distribution of a continuous response changes with a predictor. We are motivated by environmental applications in which the predictor is the dose of an exposure and the response is a health…
Since risky positions in multivariate portfolios can be offset by various choices of capital requirements that depend on the exchange rules and related transaction costs, it is natural to assume that the risk measures of random vectors are…
Bi-log-concavity of probability measures is a univariate extension of the notion of log-concavity that has been recently proposed in a statistical literature. Among other things, it has the nice property from a modelisation perspective to…