## A one-sided Vysochanskii-Petunin inequality with financial applications.(English)Zbl 1487.60045

Summary: 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.

### MSC:

 60E15 Inequalities; stochastic orderings 26D15 Inequalities for sums, series and integrals 91G70 Statistical methods; risk measures

### Keywords:

risk analysis; risk management; finance; or in banking
Full Text:

### References:

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