{"paper":{"title":"Predicting the supremum: optimality of \"stop at once or not at all\"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Pieter C. Allaart","submitted_at":"2009-12-03T10:06:19Z","abstract_excerpt":"Let X_t, 0<=t<=T be a one-dimensional stochastic process with independent and stationary increments. This paper considers the problem of stopping the process X_t \"as close as possible\" to its eventual supremum M_T:=sup{X_t: 0<=t<=T}, when the reward for stopping with a stopping time tau<=T is a nonincreasing convex function of M_T-X_tau. Under fairly general conditions on the process X_t, it is shown that the optimal stopping time tau is of \"bang-bang\" form: it is either optimal to stop at time 0 or at time T. For the case of random walk, the rule tau=T is optimal if the steps of the walk stoc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0615","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"}