Bounding the Expectation of Convex Functions with Limited Distribution Information.

Abstract

This paper considers bounds on the expectation of a convex function of a random variable when only limited information is available about the underlying distribution. The problem is presented as a generalized moment problem. A special class of functions is shown to have an easily computable solution to this problem with first and second moment constraints. Extensions are given for general convex functions on finite intervals or with finitely valued recession functions. Keywords: Integration; Stochastic programming; Moment problem; Duality; Approximation.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1987
Accession Number
ADA186147

Entities

People

  • John R. Birge
  • Jose H. Dula

Organizations

  • University of Michigan

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Applied Mathematics
  • Chebyshev Approximations
  • Computer Programming
  • Convex Sets
  • Distribution Functions
  • Engineering
  • Gaussian Quadrature
  • Inequalities
  • Integrals
  • Intervals
  • Linear Programming
  • Mathematical Programming
  • Mathematics
  • Optimization
  • Probability
  • Random Variables
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Operations Research