Bounding Conditional Value-at-Risk via Auxiliary Distributions with Bounded Discrepancies
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912510455578624 |
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| author | Pariente, Yaacov Indelman, Vadim |
| author_facet | Pariente, Yaacov Indelman, Vadim |
| contents | In this paper, we develop a theoretical framework for bounding the CVaR of a random variable $X$ using another related random variable $Y$, under assumptions on their cumulative and density functions. Our results yield practical tools for approximating $\operatorname{CVaR}_α(X)$ when direct information about $X$ is limited or sampling is computationally expensive, by exploiting a more tractable or observable random variable $Y$. Moreover, the derived bounds provide interpretable concentration inequalities that quantify how the tail risk of $X$ can be controlled via $Y$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18129 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bounding Conditional Value-at-Risk via Auxiliary Distributions with Bounded Discrepancies Pariente, Yaacov Indelman, Vadim Statistics Theory In this paper, we develop a theoretical framework for bounding the CVaR of a random variable $X$ using another related random variable $Y$, under assumptions on their cumulative and density functions. Our results yield practical tools for approximating $\operatorname{CVaR}_α(X)$ when direct information about $X$ is limited or sampling is computationally expensive, by exploiting a more tractable or observable random variable $Y$. Moreover, the derived bounds provide interpretable concentration inequalities that quantify how the tail risk of $X$ can be controlled via $Y$. |
| title | Bounding Conditional Value-at-Risk via Auxiliary Distributions with Bounded Discrepancies |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2507.18129 |