Lambda R{\'e}nyi entropic value-at-risk

Zhenfeng Zou

Papers from arXiv.org

Abstract: This paper introduces the Lambda extension of the R\'{e}nyi entropic value-at-risk ($\Lambda$-EVaR), a novel family of risk measures that unifies the flexible confidence level structure of the $\Lambda$-framework with the higher-moment sensitivity of EVaR. We define $\Lambda$-EVaR, establish its foundational properties including monotonicity, cash subadditivity, and quasi-convexity, and provide a complete axiomatic characterization showing that convexity, concavity in mixtures and cash additivity hold only when $\Lambda$ is constant. A dual representation and an extended Rockafellar-Uryasev-type formula are derived, enabling efficient computation. We further analyze the worst-case behavior of $\Lambda$-EVaR under Wasserstein and mean-variance uncertainty, obtaining closed-form expressions that reveal its robustness properties. The proposed measure bridges the gap between adaptive risk tolerance and moment-sensitive risk assessment, offering a versatile tool for modern risk management.

Date: 2026-04
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