Related papers: Multivariate Optimized Certainty Equivalent Risk M…
The left tail of the implied volatility skew, coming from quotes on out-of-the-money put options, can be thought to reflect the market's assessment of the risk of a huge drop in stock prices. We analyze how this market information can be…
This paper introduces and fully characterizes the novel class of quasi-logconvex measures of risk, to stand on equal footing with the rich class of quasi-convex measures of risk. Quasi-logconvex risk measures naturally generalize logconvex…
Marginal expected shortfall is unquestionably one of the most popular systemic risk measures. Studying its extreme behaviour is particularly relevant for risk protection against severe global financial market downturns. In this context,…
Measuring risk is at the center of modern financial risk management. As the world economy is becoming more complex and standard modeling assumptions are violated, the advanced artificial intelligence solutions may provide the right tools to…
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…
In this paper, we refine and generalize closed forms for worst-case law invariant convex risk measures with uncertainty sets based on: i) closed balls under $p$-norms and Wasserstein distance; and ii) moment constraints involving mean and…
We develop a framework for convexifying a fairly general class of optimization problems. Under additional assumptions, we analyze the suboptimality of the solution to the convexified problem relative to the original nonconvex problem and…
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…
A method is presented to tackle the sign problem in the simulations of systems having indefinite or complex-valued measures. In general, this new approach is shown to yield statistical errors smaller than the crude Monte Carlo using…
In this paper monetary risk measures that are positively superhomogeneous, called star-shaped risk measures, are characterized and their properties studied. The measures in this class, which arise when the controversial subadditivity…
All multivariate extensions of the univariate theory of risk measurement run into the same fundamental problem of the absence, in dimension d > 1, of a canonical ordering of Rd. Based on measure transportation ideas, several attempts have…
The aim of this paper is to investigate risk-averse and distributionally robust modeling of Stochastic Optimal Control (SOC) and Markov Decision Process (MDP). We discuss construction of conditional nested risk functionals, a particular…
The financial crisis has dramatically demonstrated that the traditional approach to apply univariate monetary risk measures to single institutions does not capture sufficiently the perilous systemic risk that is generated by the…
Having a perfect model to compute the optimal policy is often infeasible in reinforcement learning. It is important in high-stakes domains to quantify and manage risk induced by model uncertainties. Entropic risk measure is an exponential…
In predictive modeling with simulation or machine learning, it is critical to accurately assess the quality of estimated values through output analysis. In recent decades output analysis has become enriched with methods that quantify the…
It is shown that the axioms for coherent risk measures imply that whenever there is an asset in a portfolio that dominates the others in a given sample (which happens with finite probability even for large samples), then this portfolio…
Several authors have recently developed risk-sensitive policy gradient methods that augment the standard expected cost minimization problem with a measure of variability in cost. These studies have focused on specific risk-measures, such as…
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…
We tackle the problem of estimating risk measures of the infinite-horizon discounted cost within a Markov cost process. The risk measures we study include variance, Value-at-Risk (VaR), and Conditional Value-at-Risk (CVaR). First, we show…
Optimal uncertainty quantification (OUQ) is a framework for numerical extreme-case analysis of stochastic systems with imperfect knowledge of the underlying probability distribution. This paper presents sufficient conditions under which an…