Buffered and Reduced Multidimensional Distribution Functions and Their Application in Optimization

Bogdan Grechuk, Michael Zabarankin, Alexander Mafusalov, Stan Uryasev

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)403-426
Number of pages24
JournalOptimization Letters
Volume18
Issue number2
DOIs
StatePublished - Mar 2024

Keywords

  • BPOE
  • Buffered probability of exceedance
  • CDF
  • Conditional value-at-risk
  • Cumulative distribution function
  • Probability of exceedance

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