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Optimized Certainty Equivalent Risk Minimization Using Samples: Algorithms, Convergence Rates, and Applications — arXiv:2608.07113

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.07113
License (as archived): CC0-1.0
Archived: 2026-10-19T11:04:02.651Z
SHA-256 of the archived text: 84769b1e6ad9101e80aea2287d451305dbc170937d2e2a02e2f829a32533d675
Stable URL of this page: https://metraipolis.com/documento/dc_bb2bdffe4f04

How to cite

Optimized Certainty Equivalent Risk Minimization Using Samples: Algorithms, Convergence Rates, and Applications — arXiv:2608.07113 — arXiv (en), https://arxiv.org/abs/2608.07113 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_bb2bdffe4f04 (Metraipolis archive dc_bb2bdffe4f04, sha256 84769b1e6ad9101e80aea2287d451305dbc170937d2e2a02e2f829a32533d675)

BibTeX

@misc{dcbb2bdffe4f04,
  title = {Optimized Certainty Equivalent Risk Minimization Using Samples: Algorithms, Convergence Rates, and Applications — arXiv:2608.07113},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.07113},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_bb2bdffe4f04; sha256 84769b1e6ad9101e80aea2287d451305dbc170937d2e2a02e2f829a32533d675},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.07113. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We consider the optimization of the Optimized Certainty Equivalent (OCE) risk, with applications including portfolio optimization in finance, and uncertainty quantification, classification, and regression in machine learning. Our contributions cover popular special cases of OCE, such as entropic risk, mean-variance risk, and smooth variants of Conditional Value-at-Risk. Our treatment sets out the conditions that facilitate the extension of OCE to unbounded r.v.s.. We provide a useful characterization of OCE that links OCE to utility-based shortfall risk (UBSR). Our characterization enables us to form an OCE estimator from the classic sample-average approximation (SAA) of UBSR. We derive mean-squared error (MSE) bounds for our proposed OCE estimator. For OCE optimization, we first derive an expression for the OCE gradient using the characterization linking OCE to UBSR. This expression serves as the basis for a gradient estimator for the OCE. We derive non-asymptotic bounds on the MSE for the proposed OCE gradient estimator. We incorporate the aforementioned gradient estimator into a stochastic gradient (SG) algorithm to optimize OCE and quantify its convergence rate using non-asymptotic bounds that we derive. Finally, we present three experiments that use our OCE optimization algorithm to solve portfolio optimization and uncertainty quantification problems.

Tema degli esploratori: statistica e scienza dei dati (retro-catalogo arXiv: annunci del 2026-08-10 in stat.ML).
Categorie arXiv: Machine Learning (stat.ML) ; Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2608.07113 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-19T11:02:26.977Z dalla pagina https://arxiv.org/catchup/stat.ML/2026-08-10?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).