Sample Average Approximation of Risk-Averse Stochastic Programs

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dc.contributor.author Wang, Wei en_US
dc.date.accessioned 2008-02-07T18:37:22Z
dc.date.available 2008-02-07T18:37:22Z
dc.date.issued 2007-08-17 en_US
dc.identifier.uri http://hdl.handle.net/1853/19784
dc.description.abstract 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. en_US
dc.publisher Georgia Institute of Technology en_US
dc.subject Expected value constrained program en_US
dc.subject Mean absolute deviation en_US
dc.subject Conditional value-at-risk en_US
dc.subject Portfolio optimization en_US
dc.subject Supply chain network design en_US
dc.subject Stochastic min-max program en_US
dc.subject.lcsh Stochastic processes
dc.title Sample Average Approximation of Risk-Averse Stochastic Programs en_US
dc.type Dissertation en_US
dc.description.degree Ph.D. en_US
dc.contributor.department Industrial and Systems Engineering en_US
dc.description.advisor Committee Chair: Ahmed, Shabbir; Committee Member: Deng, Shijie; Committee Member: Li, Minqiang; Committee Member: Savelsbergh, Martin; Committee Member: Shapiro, Alexander en_US


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