Stochastic and Robust Optimization Approaches for Financial and Operations Engineering

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The classical optimization frameworks that serve as the basis for modeling in finance and operations management domains are often insightful and tractable. However, they often lack many significant real world aspects such as uncertainty. For example, the most common financial portfolio model used in industry is the mean-variance optimization (Markowitz) model, which is a deterministic problem and assumes that the expected prices(returns) of financial assets are known, which is not a practical assumption. In addition, other facets of real world environments when incorporated renders such models computationally intractable such as transaction costs or operational design decisions . Perhaps most importantly, decisions have to be made before parameter values are fully known and so the proper framework is to consider models that incorporate uncertainty to enable decisions that are immune or robust to uncertainty inherent in important parameters in the models. However, the consideration of both uncertainty and real world constraints results in models that are very challenging to solve. This proposal seeks to develop models and find solution methods for important financial engineering problems and operations management problems that integrate both uncertainty and real world practical constraints. In particular, the proposed research program seeks to investigate stochastic programming and robust optimization approaches for financial index tracking and spare parts management. The real world is inherently noisy and optimal robust solutions have a structure that is different than models that considers parameters to be deterministic and the proposal seeks to investigate what the appropriate optimal or approximate policies are in random environments. Algorithmic development is also an important component of the proposed research and will involve ideas from structured decomposition and robust convex optimization.