We derive a one-sided Vysochanskii-Petunin inequality, providing probability bounds for random variables analogous to those given by Cantelli’s inequality under the additional assumption of unimodality, potentially relevant for applied statistical practice across a wide range of disciplines. As a possible application of this inequality in a financial context, we examine refined bounds for the individual risk measure of Value-at-Risk, providing a potentially useful alternative benchmark with interesting regulatory implications for the Basel multiplier.

中文翻译：

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具有金融应用的单边 Vysochanskii-Petunin 不等式

我们推导出一个单边的 Vysochanskii-Petunin 不等式，提供类似于 Cantelli 不等式在单峰性附加假设下给出的随机变量的概率界限，这可能与广泛学科的应用统计实践相关。作为这种不平等在金融环境中的一种可能应用，我们研究了风险价值的个人风险度量的精细界限，提供了一个潜在有用的替代基准，对巴塞尔乘数具有有趣的监管影响。