Robust Risk Under Evolving Uncertainty: A Wasserstein Counterpart of the Entropic Value-at-Risk
An agent still learning its environment should be cautious while ignorant and bold once confident. The entropic value-at-risk captures this through a robust-optimization identity---a confidence level fixes the radius of a relative-entropy ball of alternative models---but that ball cannot reach catastrophes the nominal deems impossible, precisely what a safe agent must hedge. We instead use an optimal-transport ball and study the coherent risk measure it induces, the Wasserstein entropic value-at-risk. It has a variational dual mirroring the entropic formula (an inverse temperature becomes a transport price), occupies a definite place in the risk hierarchy, and provably accounts for the reachable catastrophes the entropic measure ignores; we verify both dualities numerically. Driving the transport radius by belief entropy then yields a closed-form robust dynamic-programming operator whose caution contracts as the belief sharpens, with a certified safety sandwich and a sharp safety switch.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Distributionally Robust XVA via Wasserstein Distance: Wrong Way Counterparty Credit and Funding Risk
This paper investigates calculations of robust XVA, in particular, credit valuation adjustment (CVA) and funding valuation adjustment (FVA) for over-the-counter derivatives under distributional uncertainty using Wasserst…
Quantifying Risk Under Evolving Uncertainty: Belief-Dependent Robustness for Safe Sequential Decision Making
How cautious should an agent be while it is still learning its environment? We propose RATTL (Risk-Adversarial Total-Reward Learning), which ties caution to epistemic uncertainty: the agent holds a Bayesian posterior ove…
Decision MakingOutlier-Robust Wasserstein DRO
Distributionally robust optimization (DRO) is an effective approach for data-driven decision-making in the presence of uncertainty. Geometric uncertainty due to~sampling or localized perturbations of data points is captu…
A note on robust convex risk measures
We study robust convex risk measures related to worst-case values under uncertainty in random variables. Our first main result characterizes the convex conjugate penalty term, which is the key to dual representations. Ou…
Uncertainty Propagation and Dynamic Robust Risk Measures
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 …