IJPAM: Volume 50, No. 2 (2009)

STOCHASTIC OPTIMIZATION AND UNCERTAINTY:
AN EXAMPLE

James A. Reneke$^1$, Sundeep Samson$^2$, Margaret M. Wiecek$^3$
$^{1,2,3}$Department of Mathematical Sciences
Clemson University
Clemson, South Carolina, 29634, USA
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]
$^3$e-mail: [email protected]


Abstract.R.T. Rockafellar's summary of acceptable approaches to stochatic optimization does not allow for uncertainty in F.H. Knight's sense, i.e., parameter variability with no distribution. A two level decision model, with the upper level decision model based on second order statistics of system performance and the lower level decision model a stochastic optimization problem, offers an opportunity for introducing Knightian uncertainty into the general stochastic optimization problem. We will illustrate the ideas with a portfolio selection example.

Received: August 14, 2008

AMS Subject Classification: 90B50, 90C15, 90C29

Key Words and Phrases: uncertainty, coherent measure of risk

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 50
Issue: 2