Document worth reading: “Distributionally robust optimization with polynomial densities: theory, models and algorithms”

In distributionally robust optimization the probability distribution of the uncertain draw back parameters is itself uncertain, and a fictitious adversary, e.g., nature, chooses the worst distribution from inside a acknowledged ambiguity set. A typical shortcoming of most modern distributionally robust optimization models is that their ambiguity items comprise pathological discrete distribution that give nature an extreme quantity of freedom to inflict harm. We thus introduce a model new class of ambiguity items that comprise solely distributions with sum-of-squares polynomial density options of acknowledged ranges. We current that these ambiguity items are extraordinarily expressive as they conveniently accommodate distributional particulars about higher-order moments, conditional probabilities, conditional moments or marginal distributions. Exploiting the theoretical properties of a measure-based hierarchy for polynomial optimization on account of Lasserre [SIAM J. Optim. 21(3) (2011), pp. 864–885], we present that certain worst-case expectation constraints are computationally tractable under these new ambiguity items. We showcase the wise applicability of the proposed technique inside the context of a stylized portfolio optimization draw back and a hazard aggregation draw back of an insurance coverage protection agency. Distributionally robust optimization with polynomial densities: precept, models and algorithms