2019/11/21 by Jeremiah Birrell, Paul Dupuis, Birrell, Jeremiah +7
Decision Sciences · Mathematics · #FOS: Mathematics #Probabilistic and Robust Engineering Design #Probability (math.PR) #Risk and Portfolio Optimization #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1911.09580
openalex publication_date 2019/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Rare events, and more general risk-sensitive quantities-of-interest (QoIs), are significantly impacted by uncertainty in the tail behavior of a distribution. Uncertainty in the tail can take many different forms, each of which leads to a particular ambiguity set of alternative models. Distributional robustness bounds over such an ambiguity set constitute a stress-test of the model. In this paper we develop a method, utilizing Rényi-divergences, of constructing the ambiguity set that captures a user-specified form of tail-perturbation. We then obtain distributional robustness bounds (performance guarantees) for risk-sensitive QoIs over these ambiguity sets, using the known connection between Rényi-divergences and robustness for risk-sensitive QoIs. We also expand on this connection in several ways, including a generalization of the Donsker-Varadhan variational formula to Rényi divergences, and various tightness results. These ideas are illustrated through applications to uncertainty quantification in a model of lithium-ion battery failure, robustness of large deviations rate functions, and risk-sensitive distributionally robust optimization for option pricing.