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However, these conclusions hold only when the constraints are static in the sense that the risk measure is just applied to the terminal portfolio value. In this paper, we consider a portfolio optimisation problem featuring S-shaped utility and a dynamic risk constraint which is imposed throughout the entire trading horizon. Provided that the risk control policy is sufficiently strict relative to the Sharpe ratio of the asset, the trader\u2019s portfolio strategies and the resulting maximal expected utility can be effectively constrained by a dynamic risk measure. Finally, we argue that dynamic risk constraints might still be ineffective if the trader has access to a derivatives market.<\/jats:p>","DOI":"10.1007\/s10479-023-05295-5","type":"journal-article","created":{"date-parts":[[2023,4,4]],"date-time":"2023-04-04T10:39:14Z","timestamp":1680604754000},"page":"861-898","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The importance of dynamic risk constraints for limited liability operators"],"prefix":"10.1007","volume":"336","author":[{"given":"John","family":"Armstrong","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1636-8654","authenticated-orcid":false,"given":"Damiano","family":"Brigo","sequence":"additional","affiliation":[]},{"given":"Alex S. 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