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A General Projection Property for Distribution Families
Yao-Liang Yu · Yuxi Li · Dale Schuurmans · Csaba Szepesvari

Tue Dec 08 07:00 PM -- 11:59 PM (PST) @

We prove that linear projections between distribution families with fixed first and second moments are surjective, regardless of dimension. We further extend this result to families that respect additional constraints, such as symmetry, unimodality and log-concavity. By combining our results with classic univariate inequalities, we provide new worst-case analyses for natural risk criteria arising in different fields. One discovery is that portfolio selection under the worst-case value-at-risk and conditional value-at-risk criteria yields identical portfolios.

Author Information

Yao-Liang Yu (University of Waterloo)
Yuxi Li (University of Alberta)
Dale Schuurmans (Google Brain & University of Alberta)
Csaba Szepesvari (University of Alberta)

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