{"paper":{"title":"Nonsmooth Obstacles and Killed Resolvents in Reflected Stochastic Control","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.OC","authors_text":"Jiguang Yu, Louis Shuo Wang, Ye Liang","submitted_at":"2026-06-19T16:18:17Z","abstract_excerpt":"We study an infinite-horizon optimal stopping problem for a normally reflected two-dimensional diffusion in the quadrant with nonsmooth max-type payoff \\(G(x_1,x_2)=x_1\\vee\\alpha x_2\\). The main novelty is a measure-valued variational formulation: the stopping gain \\(\\Gamma=c+rG-\\mathcal LG\\) is shown to be a signed Radon measure whose singular component is supported on the kink diagonal \\(\\{x_1=\\alpha x_2\\}\\), and this component is computed explicitly. We prove that the value admits the killed-resolvent representation \\[\n  V=G-R_r^{\\mathcal C}\\Gamma, \\] where the reflected diffusion is killed"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21575","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.21575/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}