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Sample average approximation of risk-averse stochastic programs.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Sample average approximation of risk-averse stochastic programs./
Author:	Wang, Wei.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2007,
Description:	104 p.
Notes:	Source: Dissertations Abstracts International, Volume: 69-09, Section: B.
Contained By:	Dissertations Abstracts International69-09B.
Subject:	Industrial engineering. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3294570
ISBN:	9780549388654

Sample average approximation of risk-averse stochastic programs.
Wang, Wei.

Sample average approximation of risk-averse stochastic programs. - Ann Arbor : ProQuest Dissertations & Theses, 2007 - 104 p.

Source: Dissertations Abstracts International, Volume: 69-09, Section: B.

Thesis (Ph.D.)--Georgia Institute of Technology, 2007.

Sample average approximation (SAA) is a well-known solution methodology for traditional stochastic programs which are risk neutral in the sense that they consider optimization of expectation functionals. In this thesis we establish sample average approximation methods for two classes of non-traditional stochastic programs. The first class is that of stochastic min-max programs, i.e., min-max problems with expected value objectives, and the second class is that of expected value constrained stochastic programs. We specialize these SAA methods for risk-averse stochastic problems with a bi-criteria objective involving mean and mean absolute deviation, and those with constraints on conditional value-at-risk. For the proposed SAA methods, we prove that the results of the SAA problem converge exponentially fast to their counterparts for the true problem as the sample size increases. We also propose implementation schemes which return not only candidate solutions but also statistical upper and lower bound estimates on the optimal value of the true problem. We apply the proposed methods to solve portfolio selection and supply chain network design problems. Our computational results reflect good performance of the proposed SAA schemes. We also investigate the effect of various types of risk-averse stochastic programming models in controlling risk in these problems.

ISBN: 9780549388654Subjects--Topical Terms:

526216
Industrial engineering.
Subjects--Index Terms:

Conditional value-at-risk

Sample average approximation of risk-averse stochastic programs.
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245 1 0 $a Sample average approximation of risk-averse stochastic programs.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2007
300 $a 104 p.
500 $a Source: Dissertations Abstracts International, Volume: 69-09, Section: B.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisor: Ahmed, Shabbir.
502 $a Thesis (Ph.D.)--Georgia Institute of Technology, 2007.
520 $a Sample average approximation (SAA) is a well-known solution methodology for traditional stochastic programs which are risk neutral in the sense that they consider optimization of expectation functionals. In this thesis we establish sample average approximation methods for two classes of non-traditional stochastic programs. The first class is that of stochastic min-max programs, i.e., min-max problems with expected value objectives, and the second class is that of expected value constrained stochastic programs. We specialize these SAA methods for risk-averse stochastic problems with a bi-criteria objective involving mean and mean absolute deviation, and those with constraints on conditional value-at-risk. For the proposed SAA methods, we prove that the results of the SAA problem converge exponentially fast to their counterparts for the true problem as the sample size increases. We also propose implementation schemes which return not only candidate solutions but also statistical upper and lower bound estimates on the optimal value of the true problem. We apply the proposed methods to solve portfolio selection and supply chain network design problems. Our computational results reflect good performance of the proposed SAA schemes. We also investigate the effect of various types of risk-averse stochastic programming models in controlling risk in these problems.
590 $a School code: 0078.
650 4 $a Industrial engineering. $3 526216
650 4 $a Operations research. $3 547123
653 $a Conditional value-at-risk
653 $a Expected value-constrained programs
653 $a Mean absolute deviation
653 $a Portfolio optimization
653 $a Sample average approximation
653 $a Stochastic min-max programs
653 $a Supply chain network design
690 $a 0546
690 $a 0796
710 2 $a Georgia Institute of Technology. $3 696730
773 0 $t Dissertations Abstracts International $g 69-09B.
790 $a 0078
791 $a Ph.D.
792 $a 2007
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3294570