{"ID":2890775,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.18129","arxiv_id":"2507.18129","title":"Bounding Conditional Value-at-Risk via Auxiliary Distributions with Bounded Discrepancies","abstract":"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 $Y$.","short_abstract":"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 lim...","url_abs":"https://arxiv.org/abs/2507.18129","url_pdf":"https://arxiv.org/pdf/2507.18129v2","authors":"[\"Yaacov Pariente\",\"Vadim Indelman\"]","published":"2025-07-24T06:34:24Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}