{"paper":{"title":"Optimal stopping under adverse nonlinear expectation and related games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","q-fin.PR"],"primary_cat":"math.OC","authors_text":"Jianfeng Zhang, Marcel Nutz","submitted_at":"2012-12-10T17:23:14Z","abstract_excerpt":"We study the existence of optimal actions in a zero-sum game $\\inf_{\\tau}\\sup_PE^P[X_{\\tau}]$ between a stopper and a controller choosing a probability measure. This includes the optimal stopping problem $\\inf_{\\tau}\\mathcal{E}(X_{\\tau})$ for a class of sublinear expectations $\\mathcal{E}(\\cdot)$ such as the $G$-expectation. We show that the game has a value. Moreover, exploiting the theory of sublinear expectations, we define a nonlinear Snell envelope $Y$ and prove that the first hitting time $\\inf\\{t:Y_t=X_t\\}$ is an optimal stopping time. The existence of a saddle point is shown under a co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2140","kind":"arxiv","version":3},"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"}