Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distributional Robustness and Uncertainty Quantification for Rare Events   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 R\'enyi-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 R\'enyi-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 R\'enyi 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.

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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con