TY - JOUR
T1 - Buffered and Reduced Multidimensional Distribution Functions and Their Application in Optimization
AU - Grechuk, Bogdan
AU - Zabarankin, Michael
AU - Mafusalov, Alexander
AU - Uryasev, Stan
N1 - Publisher Copyright:
© The Author(s) 2023.
PY - 2024/3
Y1 - 2024/3
N2 - For a random variable, superdistribution has emerged as a valuable probability concept. Similar to cumulative distribution function (CDF), it uniquely defines the random variable and can be evaluated with a simple one-dimensional minimization formula. This work leverages the structure of that formula to introduce buffered CDF (bCDF) and reduced CDF (rCDF) for random vectors. bCDF and rCDF are shown to be the minimal Schur-convex upper bound and the maximal Schur-concave lower bound of the multivariate CDF, respectively. Special structure of bCDF and rCDF is used to construct an algorithm for solving optimization problems with bCDF and rCDF in objective or constraints. The efficiency of the algorithm is demonstrated in a case study on optimization of a collateralized debt obligation with bCDF functions in constraints.
AB - For a random variable, superdistribution has emerged as a valuable probability concept. Similar to cumulative distribution function (CDF), it uniquely defines the random variable and can be evaluated with a simple one-dimensional minimization formula. This work leverages the structure of that formula to introduce buffered CDF (bCDF) and reduced CDF (rCDF) for random vectors. bCDF and rCDF are shown to be the minimal Schur-convex upper bound and the maximal Schur-concave lower bound of the multivariate CDF, respectively. Special structure of bCDF and rCDF is used to construct an algorithm for solving optimization problems with bCDF and rCDF in objective or constraints. The efficiency of the algorithm is demonstrated in a case study on optimization of a collateralized debt obligation with bCDF functions in constraints.
KW - BPOE
KW - Buffered probability of exceedance
KW - CDF
KW - Conditional value-at-risk
KW - Cumulative distribution function
KW - Probability of exceedance
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U2 - 10.1007/s11590-023-02045-1
DO - 10.1007/s11590-023-02045-1
M3 - Article
AN - SCOPUS:85173975255
SN - 1862-4472
VL - 18
SP - 403
EP - 426
JO - Optimization Letters
JF - Optimization Letters
IS - 2
ER -