Resource title

A Semidefinite programming approach to optimal moment bounds for convex classes of distributions (RV of 2002/54/TM)

Resource image

image for OpenScout resource :: A Semidefinite programming approach to optimal moment bounds for convex classes of distributions (RV of 2002/54/TM)

Resource description

The author provides an optimization framework for computing optimal upper and lower bounds on functional expectations of distributions with special properties, given moment constraints. Bertsimas and Popescu [3, 4] have already shown how to obtain optimal moment inequalities for arbitrary distributions via semidefinite programming. These bounds are not sharp if the underlying distributions possess additional structural properties, including symmetry, unimodality, convexity or smoothness. For convex distribution classes that are in some sense generated by an appropriate parametric family, the author uses conic duality to show how optimal moment bounds can be efficiently computed as semidefinite programs. In particular, she obtains generalizations of Chebyshev's inequality for symmetric and unimodal distributions, and provide numerical calculations to compare these bounds given higher order moments. She also extends these results for multivariate distributions.

Resource author

Resource publisher

Resource publish date

Resource language

en

Resource content type

application/pdf

Resource resource URL

http://flora.insead.edu/fichiersti_wp/inseadwp2004/2004-30.pdf

Resource license

Copyright INSEAD. All rights reserved