Robust Risk Under Evolving Uncertainty: A Wasserstein Counterpart of the Entropic Value-at-Risk

Source

• Source name: arXiv
• Source kind: paper
• Authors / organization: Deep Kumar Ganguly, Jan Křetínský
• Venue: arXiv: cs.AI
• Published: 2026-08-19
• Collected: 2026-08-20
• URL: http://arxiv.org/abs/2608.19073v1
• PDF: https://arxiv.org/pdf/2608.19073v1
• DOI: UNKNOWN
• Registry group: academic_apis_and_preprints
• Evidence role: canonical_academic_index
• Language: en
• Country / region: UNKNOWN

Plain-Language Brief

The paper proposes a new risk measure called Wasserstein Entropic Value-at-Risk (WEVaR) for an agent learning its environment. The WEVaR is designed to account for the reachable catastrophes that the current entropic value-at-risk ignores. It uses optimal transport theory and belief entropy to create a dynamic programming operator that adjusts caution based on the sharpness of the agent's beliefs.

What the Document Says

• The paper discusses a new coherent risk measure called Wasserstein Entropic Value-at-Risk (WEVaR).
• It is proposed as an improvement over the current entropic value-at-risk, as it addresses the shortcomings of the latter in accounting for reachable catastrophes.
• The WEVaR uses optimal transport theory and belief entropy to create a dynamic programming operator.
• This operator adjusts caution based on the sharpness of the agent's beliefs.

Key Concepts Mentioned

• Wasserstein Entropic Value-at-Risk
• optimal transport theory
• belief entropy
• dynamic programming operator

Claims Made by the Document

• The WEVaR improves upon the current entropic value-at-risk by accounting for reachable catastrophes.
• The dynamic programming operator adjusts caution based on the sharpness of the agent's beliefs.

Evidence Used

• The paper presents a new coherent risk measure, the WEVaR, and discusses its properties.

Methods / Approach

• Optimal transport theory
• Belief entropy
• Dynamic programming

Limitations Stated by the Authors

UNKNOWN

Limitations Noted by the Agent

Agent interpretation — not from the source.

UNKNOWN

Open Questions

UNKNOWN

Notes for Future Q&A

May include interpretation. Labeled where it does.

UNKNOWN

Raw Abstract / Excerpt

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.