Modeling stochastic dependencies and their impact on optimal decision making
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This research addresses three important questions for solving a general stochastic optimization problem: proper modeling of the uncertainties and their interactions, use of decomposition techniques to solve the resulting optimization problems, and the impact of stochastic dependencies to the optimal solution. In particular, we develop sampling methodologies for scenario generation that preserve the cointegration properties of financial time series, create a new conditional decision-dependent probability model for the lifetime of components in nuclear power plants, define the corresponding stochastic optimization problems, and construct decomposition algorithms to solve them. We investigate the impact of the input (in terms of different stochastic dependencies) to the solution of the corresponding optimization problem. For the last issue we concentrate on the general financial asset allocation problem.