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Abstract
When decisions are based on empirical observations, a trade-off arises between flexibility of the decision and ability to generalize to new situations. In this paper, we focus on decisions that are obtained by the empirical minimization of the Conditional Value-at-Risk (CVaR) and argue that in CVaR the trade-off between flexibility and generalization can be understood on the ground of theoretical results under very general assumptions on the system that generates the observations. The results have implications on topics related to order and structure selection in various applications where the CVaR risk-measure is used. A study on a portfolio optimization problem with real data demonstrates our results.
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Authors and Affiliations
Department of Information Engineering, University of Brescia, via Branze 38, 25123, Brescia, Italy
Giorgio Arici, Marco C. Campi, Algo Carè, Marco Dalai & Federico A. Ramponi
- Giorgio Arici
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- Marco C. Campi
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- Algo Carè
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- Marco Dalai
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- Federico A. Ramponi
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Correspondence toGiorgio Arici,Marco C. Campi,Algo Carè,Marco Dalai orFederico A. Ramponi.
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This research was partially supported by Regione Lombardia under Grant MoSoRe E81B19000840007.
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Arici, G., Campi, M.C., Carè, A.et al. A Theory of the Risk for Empirical CVaR with Application to Portfolio Selection.J Syst Sci Complex34, 1879–1894 (2021). https://doi.org/10.1007/s11424-021-1229-3
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