Submodular risk measures

Ruodu Wang and Jingcheng Yu

Papers from arXiv.org

Abstract: We study submodularity for law-invariant functionals, with particular attention to convex risk measures. Expected losses are modular, and certainty equivalents are submodular exactly when the loss function is convex. Law-invariant coherent risk measures are submodular exactly when they are coherent distortion risk measures, including Expected Shortfall (ES), and several deviation measures are also submodular. Beyond positive homogeneity, submodularity is restrictive for convex risk measures. We give a complete characterization for shortfall risk measures via the Arrow--Pratt measure of risk aversion, show that optimized certainty equivalents are always submodular, and prove that adjusted Expected Shortfall (AES) is submodular only when it reduces to ES. An empirical illustration for daily US equity returns finds no ES submodularity violations, many Value-at-Risk (VaR) violations, and relatively few AES violations.

Date: 2026-03, Revised 2026-04
New Economics Papers: this item is included in nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2603.01232 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2603.01232

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().