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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2604.10657 |
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| _version_ | 1866910122600562688 |
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| author | Zou, Zhenfeng |
| author_facet | Zou, Zhenfeng |
| contents | This paper introduces the Lambda extension of the Rényi entropic value-at-risk ($Λ$-EVaR), a novel family of risk measures that unifies the flexible confidence level structure of the $Λ$-framework with the higher-moment sensitivity of EVaR. We define $Λ$-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 $Λ$ 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 $Λ$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10657 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lambda R{é}nyi entropic value-at-risk Zou, Zhenfeng Risk Management This paper introduces the Lambda extension of the Rényi entropic value-at-risk ($Λ$-EVaR), a novel family of risk measures that unifies the flexible confidence level structure of the $Λ$-framework with the higher-moment sensitivity of EVaR. We define $Λ$-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 $Λ$ 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 $Λ$-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. |
| title | Lambda R{é}nyi entropic value-at-risk |
| topic | Risk Management |
| url | https://arxiv.org/abs/2604.10657 |