{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:II3ZCD76ARSSYY6FVZEMIXOL5C","short_pith_number":"pith:II3ZCD76","schema_version":"1.0","canonical_sha256":"4237910ffe04652c63c5ae48c45dcbe8bb71a8b74b1ec4c413330aa68eddf9ad","source":{"kind":"arxiv","id":"1201.1788","version":2},"attestation_state":"computed","paper":{"title":"Complete duality for quasiconvex dynamic risk measures on modules of the $L^{p}$-type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"q-fin.RM","authors_text":"Marco Frittelli, Marco Maggis","submitted_at":"2012-01-09T14:51:08Z","abstract_excerpt":"In the conditional setting we provide a complete duality between quasiconvex risk measures defined on $L^{0}$ modules of the $L^{p}$ type and the appropriate class of dual functions. This is based on a general result which extends the usual Penot-Volle representation for quasiconvex real valued maps."},"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":"1201.1788","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.RM","submitted_at":"2012-01-09T14:51:08Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"d29c56ab5921b782e69ead5b2f0bba18510092ae470d0f5656b51b4741541b7e","abstract_canon_sha256":"9455db0ace5da549c583285ee52aada04bd15b8c376061470b48c8c35145c7e0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:16.747806Z","signature_b64":"gAKd5SjmpeJpKs8tGNoIL46/AsnRk+hj4jYLFDXMvQG5QNCk44Uiu6fq/EkWtZn+IzXXsPAGBHnRopUmC9n+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4237910ffe04652c63c5ae48c45dcbe8bb71a8b74b1ec4c413330aa68eddf9ad","last_reissued_at":"2026-05-18T03:46:16.746689Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:16.746689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Complete duality for quasiconvex dynamic risk measures on modules of the $L^{p}$-type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"q-fin.RM","authors_text":"Marco Frittelli, Marco Maggis","submitted_at":"2012-01-09T14:51:08Z","abstract_excerpt":"In the conditional setting we provide a complete duality between quasiconvex risk measures defined on $L^{0}$ modules of the $L^{p}$ type and the appropriate class of dual functions. This is based on a general result which extends the usual Penot-Volle representation for quasiconvex real valued maps."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1788","kind":"arxiv","version":2},"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":"1201.1788","created_at":"2026-05-18T03:46:16.746801+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.1788v2","created_at":"2026-05-18T03:46:16.746801+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1788","created_at":"2026-05-18T03:46:16.746801+00:00"},{"alias_kind":"pith_short_12","alias_value":"II3ZCD76ARSS","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_16","alias_value":"II3ZCD76ARSSYY6F","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_8","alias_value":"II3ZCD76","created_at":"2026-05-18T12:27:09.501522+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/II3ZCD76ARSSYY6FVZEMIXOL5C","json":"https://pith.science/pith/II3ZCD76ARSSYY6FVZEMIXOL5C.json","graph_json":"https://pith.science/api/pith-number/II3ZCD76ARSSYY6FVZEMIXOL5C/graph.json","events_json":"https://pith.science/api/pith-number/II3ZCD76ARSSYY6FVZEMIXOL5C/events.json","paper":"https://pith.science/paper/II3ZCD76"},"agent_actions":{"view_html":"https://pith.science/pith/II3ZCD76ARSSYY6FVZEMIXOL5C","download_json":"https://pith.science/pith/II3ZCD76ARSSYY6FVZEMIXOL5C.json","view_paper":"https://pith.science/paper/II3ZCD76","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.1788&json=true","fetch_graph":"https://pith.science/api/pith-number/II3ZCD76ARSSYY6FVZEMIXOL5C/graph.json","fetch_events":"https://pith.science/api/pith-number/II3ZCD76ARSSYY6FVZEMIXOL5C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/II3ZCD76ARSSYY6FVZEMIXOL5C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/II3ZCD76ARSSYY6FVZEMIXOL5C/action/storage_attestation","attest_author":"https://pith.science/pith/II3ZCD76ARSSYY6FVZEMIXOL5C/action/author_attestation","sign_citation":"https://pith.science/pith/II3ZCD76ARSSYY6FVZEMIXOL5C/action/citation_signature","submit_replication":"https://pith.science/pith/II3ZCD76ARSSYY6FVZEMIXOL5C/action/replication_record"}},"created_at":"2026-05-18T03:46:16.746801+00:00","updated_at":"2026-05-18T03:46:16.746801+00:00"}