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Masters Theses
Date of Award
8-1996
Degree Type
Thesis
Degree Name
Master of Science
Major
Mathematics
Major Professor
Yueh-er Kuo
Committee Members
J. Smith, C. Collins
Abstract
The idea of bounding E[g(X)], where g is a convex function of a multivariate random variable X, has received considerable attention in the literature. The need for such a bound arises from the complexities associated with computing E[g(X)], especially in a stochastic programming setting, when the dimension of X is large. The first contribution in this area was Jensen's inequality (1906). The purpose here is to discuss the Ist order bounds derived by Madansky (1959), Ben-Tal and Hochman's (1972) refinement of the Madansky bound using additional information, and Gassman and Ziemba's (1986) extension of the Madansky bound. An example of bounding E[f(X)], where f is not necessarily convex, will also be discussed.
Recommended Citation
Yates, Phillip D., "Bounds on the expectation of a convex function of a multivariate random variable. " Master's Thesis, University of Tennessee, 1996.
https://trace.tennessee.edu/utk_gradthes/11014