{"paper":{"title":"Local martingale deflators for asset processes stopped at a default time $S^\\tau$ or right before $S^{\\tau-}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"q-fin.PR","authors_text":"Shiqi Song","submitted_at":"2014-05-18T08:56:02Z","abstract_excerpt":"Let $\\mathbb{F}\\subset \\mathbb{G}$ be two filtrations and $S$ be a $\\mathbb{F}$ semimartingale possessing a $\\mathbb{F}$ local martingale deflator. Consider $\\tau$ a $\\mathbb{G}$ stopping time. We study the problem whether $S^{\\tau-}$ or $S^{\\tau}$ can have $\\mathbb{G}$ local martingale deflators. A suitable theoretical framework is set up in this paper, within which necessary/sufficient conditions for the problem to be solved have been proved. Under these conditions, we will construct $\\mathbb{G}$ local martingale deflators for $S^{\\tau-}$ or for $S^{\\tau}$. Among others, it is proved that $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4474","kind":"arxiv","version":4},"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"}