{"paper":{"title":"On the Robust Optimal Stopping Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","math.OC","q-fin.PR"],"primary_cat":"math.PR","authors_text":"Erhan Bayraktar, Song Yao","submitted_at":"2013-01-01T14:26:49Z","abstract_excerpt":"We study a robust optimal stopping problem with respect to a set $\\cP$ of mutually singular probabilities. This can be interpreted as a zero-sum controller-stopper game in which the stopper is trying to maximize its pay-off while an adverse player wants to minimize this payoff by choosing an evaluation criteria from $\\cP$. We show that the \\emph{upper Snell envelope $\\ol{Z}$} of the reward process $Y$ is a supermartingale with respect to an appropriately defined nonlinear expectation $\\ul{\\sE}$, and $\\ol{Z}$ is further an $\\ul{\\sE}-$martingale up to the first time $\\t^*$ when $\\ol{Z}$ meets $Y"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0091","kind":"arxiv","version":10},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}