Derivatives and subderivatives of buffered probability of exceedance

Tong Zhang; Stan Uryasev; Yongpei Guan

doi:10.1016/j.orl.2019.02.002

Derivatives and subderivatives of buffered probability of exceedance

Tong Zhang
, Stan Uryasev
, Yongpei Guan

Applied Mathematics and Statistics

University of Florida

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

In this letter, we study the derivatives and subderivatives of buffered probability of exceedance (bPOE), in which we provide the mathematical expressions with rigorous proofs for the case when bPOE is smooth. Furthermore, we extend the study to a general non-smooth case for which a set of quasigradients are explored, under a mild assumption, i.e., the corresponding random function with respect to the decision variable is convex.

Original language	English
Pages (from-to)	130-132
Number of pages	3
Journal	Operations Research Letters
Volume	47
Issue number	2
DOIs	https://doi.org/10.1016/j.orl.2019.02.002
State	Published - Mar 2019

Keywords

Buffered probability of exceedance
CVaR
Gradient
Quasigradient

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10.1016/j.orl.2019.02.002

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abstract = "In this letter, we study the derivatives and subderivatives of buffered probability of exceedance (bPOE), in which we provide the mathematical expressions with rigorous proofs for the case when bPOE is smooth. Furthermore, we extend the study to a general non-smooth case for which a set of quasigradients are explored, under a mild assumption, i.e., the corresponding random function with respect to the decision variable is convex.",

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AU - Uryasev, Stan

AU - Guan, Yongpei

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N2 - In this letter, we study the derivatives and subderivatives of buffered probability of exceedance (bPOE), in which we provide the mathematical expressions with rigorous proofs for the case when bPOE is smooth. Furthermore, we extend the study to a general non-smooth case for which a set of quasigradients are explored, under a mild assumption, i.e., the corresponding random function with respect to the decision variable is convex.

AB - In this letter, we study the derivatives and subderivatives of buffered probability of exceedance (bPOE), in which we provide the mathematical expressions with rigorous proofs for the case when bPOE is smooth. Furthermore, we extend the study to a general non-smooth case for which a set of quasigradients are explored, under a mild assumption, i.e., the corresponding random function with respect to the decision variable is convex.

KW - Buffered probability of exceedance

KW - CVaR

KW - Gradient

KW - Quasigradient

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DO - 10.1016/j.orl.2019.02.002

M3 - Article

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SP - 130

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JO - Operations Research Letters

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ER -

Derivatives and subderivatives of buffered probability of exceedance

Abstract

Keywords

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