Distribution-free stochastic optimization: advances in solution methods and applications

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Many real-world optimization problems involve random inputs for which it is difficult to make exact distributional assumptions; among others, due to the scarcity of data, and/or the very high volatility of the available data. Distribution-free stochastic optimization refers to decision making problems where only partial knowledge of the random inputs' distribution is assumed. Distribution-free (stochastic) optimization techniques have been successfully applied to decision making problems in game theory, inventory/supply chain management, combinatorial optimization, portfolio allocation, option pricing, risk management, and actuarial science. More generally, distribution-free optimization techniques are used to make "robust" decisions; that is, decisions that "work well" in many scenarios.