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.

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