{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:BSKAJJSTZKP7QKH6RUSFMWPEC5","short_pith_number":"pith:BSKAJJST","schema_version":"1.0","canonical_sha256":"0c9404a653ca9ff828fe8d245659e4176f85e85b122f6a2b6df604e9074edf4d","source":{"kind":"arxiv","id":"1006.3224","version":6},"attestation_state":"computed","paper":{"title":"Outperforming the market portfolio with a given probability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.OC","math.PR","q-fin.PM"],"primary_cat":"q-fin.CP","authors_text":"Erhan Bayraktar, Qingshuo Song, Yu-Jui Huang","submitted_at":"2010-06-13T12:57:30Z","abstract_excerpt":"Our goal is to resolve a problem proposed by Fernholz and Karatzas [On optimal arbitrage (2008) Columbia Univ.]: to characterize the minimum amount of initial capital with which an investor can beat the market portfolio with a certain probability, as a function of the market configuration and time to maturity. We show that this value function is the smallest nonnegative viscosity supersolution of a nonlinear PDE. As in Fernholz and Karatzas [On optimal arbitrage (2008) Columbia Univ.], we do not assume the existence of an equivalent local martingale measure, but merely the existence of a local"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1006.3224","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2010-06-13T12:57:30Z","cross_cats_sorted":["math.AP","math.OC","math.PR","q-fin.PM"],"title_canon_sha256":"ab2eb038d06274a7e8b39d6d162ccc51cb126231bfc6dd4fff01ba6b49184ea0","abstract_canon_sha256":"208c3b19310aa8e5b6f1daad8d8a6a70382621b8e3b9baaa765aa3efcbc23970"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:24.514515Z","signature_b64":"Ic/wBrXwsFNkMI3/J7frfXPC/m7aG1//vB9jgOivz0QCgESaieWiIWZEGiWSXD5XQpJ/dh4o11MdYyxVJeHUDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c9404a653ca9ff828fe8d245659e4176f85e85b122f6a2b6df604e9074edf4d","last_reissued_at":"2026-05-18T03:48:24.513811Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:24.513811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Outperforming the market portfolio with a given probability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.OC","math.PR","q-fin.PM"],"primary_cat":"q-fin.CP","authors_text":"Erhan Bayraktar, Qingshuo Song, Yu-Jui Huang","submitted_at":"2010-06-13T12:57:30Z","abstract_excerpt":"Our goal is to resolve a problem proposed by Fernholz and Karatzas [On optimal arbitrage (2008) Columbia Univ.]: to characterize the minimum amount of initial capital with which an investor can beat the market portfolio with a certain probability, as a function of the market configuration and time to maturity. We show that this value function is the smallest nonnegative viscosity supersolution of a nonlinear PDE. As in Fernholz and Karatzas [On optimal arbitrage (2008) Columbia Univ.], we do not assume the existence of an equivalent local martingale measure, but merely the existence of a local"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.3224","kind":"arxiv","version":6},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1006.3224","created_at":"2026-05-18T03:48:24.513928+00:00"},{"alias_kind":"arxiv_version","alias_value":"1006.3224v6","created_at":"2026-05-18T03:48:24.513928+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.3224","created_at":"2026-05-18T03:48:24.513928+00:00"},{"alias_kind":"pith_short_12","alias_value":"BSKAJJSTZKP7","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"BSKAJJSTZKP7QKH6","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"BSKAJJST","created_at":"2026-05-18T12:26:05.355336+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BSKAJJSTZKP7QKH6RUSFMWPEC5","json":"https://pith.science/pith/BSKAJJSTZKP7QKH6RUSFMWPEC5.json","graph_json":"https://pith.science/api/pith-number/BSKAJJSTZKP7QKH6RUSFMWPEC5/graph.json","events_json":"https://pith.science/api/pith-number/BSKAJJSTZKP7QKH6RUSFMWPEC5/events.json","paper":"https://pith.science/paper/BSKAJJST"},"agent_actions":{"view_html":"https://pith.science/pith/BSKAJJSTZKP7QKH6RUSFMWPEC5","download_json":"https://pith.science/pith/BSKAJJSTZKP7QKH6RUSFMWPEC5.json","view_paper":"https://pith.science/paper/BSKAJJST","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1006.3224&json=true","fetch_graph":"https://pith.science/api/pith-number/BSKAJJSTZKP7QKH6RUSFMWPEC5/graph.json","fetch_events":"https://pith.science/api/pith-number/BSKAJJSTZKP7QKH6RUSFMWPEC5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BSKAJJSTZKP7QKH6RUSFMWPEC5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BSKAJJSTZKP7QKH6RUSFMWPEC5/action/storage_attestation","attest_author":"https://pith.science/pith/BSKAJJSTZKP7QKH6RUSFMWPEC5/action/author_attestation","sign_citation":"https://pith.science/pith/BSKAJJSTZKP7QKH6RUSFMWPEC5/action/citation_signature","submit_replication":"https://pith.science/pith/BSKAJJSTZKP7QKH6RUSFMWPEC5/action/replication_record"}},"created_at":"2026-05-18T03:48:24.513928+00:00","updated_at":"2026-05-18T03:48:24.513928+00:00"}