Higher-Order Upper Bounds on the Expectation of a Convex Function

Steftcho P. Dokov; David P. Morton

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SPEPS Preprint

Author(s):	Steftcho P. Dokov, The University of Texas at Austin David P. Morton, The University of Texas at Austin
Title:	Higher-Order Upper Bounds on the Expectation of a Convex Function
Date of Acceptance:	03.05.2002
Submission Date:	23.01.2002
Series Title:	Stochastic Programming E-Print Series (SPEPS)
Editors:	Julie L. Higle; Werner Römisch; Surrajeet Sen
Complete Preprint:	pdf (urn:nbn:de:kobv:11-10058406)
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Abstract (eng):

We develop a decreasing sequence of upper bounds on the expectation of a convex function. The n-th term in the sequence uses moments and cross-moments of up to degree n from the underlying random vector. Our work has application to a class of two-stage stochastic programs with recourse. The objective function of such a model can defy computation when: (i) the underlying distribution is assumed to be known only through a limited number of moments or (ii) the function is computationally intractable, even though the distribution is known. A tractable approximating model arises by replacing the objective function by one of our bounding elements. We justify this approach by showing that as n grows, solutions of the order-n approximation solve the true stochastic program.

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