Many real-world decision problems in engineering and management have uncertain parameters. Robust optimization methodology takes into account the uncertainty in parameters of the model in the decision-making framework. In robust optimization methodology, we assume we do not know the probability distribution of parameters, and we have partial information about parameters. Portfolio management is one of those famous applications that have an uncertain environment. So, for this application, robust methodology would be a good choice. This dissertation contains three main works as the following:\\ In the first work, we provided the combination of European options and a robust optimization model to deal with uncertainty in stock returns. We also present some interesting insights about the optimal portfolio allocation.
In the second work, we consider the mean-variance problem when the projects or stocks are subject to both return uncertainty and exogenous shocks. We develop a tractable reformulation of the problem where we minimize the variance of return and satisfy the minimum threshold of expected return.
In the last work, we use adaptive robust optimization for project selection and scheduling problems that consider the dependence of new information on earlier decisions. This approach is called multi-stage robust optimization for both exogenous and endogenous uncertainty. So, we can continue or abandon the selected projects after the realization of detailed costs and benefits of different phases of projects.
Operations Research and Engineering Management
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Ashrafi, Hedieh and Thiele, Aurelie, "Robust Optimization with Recourse in Portfolio Management: Theory and Applications to Stocks and Projects" (2021). Operations Research and Engineering Management Theses and Dissertations. 19.