{"paper":{"title":"Optimal multiple stopping time problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Elisabeth Rouy-Mironescu, Magdalena Kobylanski, Marie-Claire Quenez","submitted_at":"2009-10-15T06:49:38Z","abstract_excerpt":"We study the optimal multiple stopping time problem defined for each stopping time $S$ by $v(S)=\\operatorname {ess}\\sup_{\\tau_1,...,\\tau_d\\geq S}E[\\psi(\\tau_1,...,\\tau_d)|\\mathcal{F}_S]$. The key point is the construction of a new reward $\\phi$ such that the value function $v(S)$ also satisfies $v(S)=\\operatorname {ess}\\sup_{\\theta\\geq S}E[\\phi(\\theta)|\\mathcal{F}_S]$. This new reward $\\phi$ is not a right-continuous adapted process as in the classical case, but a family of random variables. For such a reward, we prove a new existence result for optimal stopping times under weaker assumptions "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2788","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"}