{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:CLWNHXOL3NLUGF5LPZ3YW3LSIR","short_pith_number":"pith:CLWNHXOL","schema_version":"1.0","canonical_sha256":"12ecd3ddcbdb574317ab7e778b6d72447a7ed48e24803ad01c47510f0fd242d5","source":{"kind":"arxiv","id":"1805.05259","version":1},"attestation_state":"computed","paper":{"title":"The strong Fatou property of risk measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-fin.RM","authors_text":"Foivos Xanthos, Niushan Gao, Shengzhong Chen","submitted_at":"2018-05-14T16:15:43Z","abstract_excerpt":"In this paper, we explore several Fatou-type properties of risk measures. The paper continues to reveal that the strong Fatou property, which was introduced in [17], seems to be most suitable to ensure nice dual representations of risk measures. Our main result asserts that every quasiconvex law-invariant functional on a rearrangement invariant space $\\mathcal{X}$ with the strong Fatou property is $\\sigma(\\mathcal{X},L^\\infty)$ lower semicontinuous and that the converse is true on a wide range of rearrangement invariant spaces. We also study inf-convolutions of law-invariant or surplus-invaria"},"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":"1805.05259","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.RM","submitted_at":"2018-05-14T16:15:43Z","cross_cats_sorted":[],"title_canon_sha256":"2c3691732ee9c91d6bdc5b39157a526bc295ce69561afb699bf1508683a74da8","abstract_canon_sha256":"58c670bb42a9d44cc2e4867dbb68d78c4da72fd974832fd4299c180a436db32f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:03.588802Z","signature_b64":"UPyV+2JWMBXTsrTy024mTPW0BuGo0k2k4Bf8bdY5e1gpxgSisZrfTVH72jV/5l+S2sOkazxiM4+gtuUdPOB5CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12ecd3ddcbdb574317ab7e778b6d72447a7ed48e24803ad01c47510f0fd242d5","last_reissued_at":"2026-05-18T00:16:03.588430Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:03.588430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The strong Fatou property of risk measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-fin.RM","authors_text":"Foivos Xanthos, Niushan Gao, Shengzhong Chen","submitted_at":"2018-05-14T16:15:43Z","abstract_excerpt":"In this paper, we explore several Fatou-type properties of risk measures. The paper continues to reveal that the strong Fatou property, which was introduced in [17], seems to be most suitable to ensure nice dual representations of risk measures. Our main result asserts that every quasiconvex law-invariant functional on a rearrangement invariant space $\\mathcal{X}$ with the strong Fatou property is $\\sigma(\\mathcal{X},L^\\infty)$ lower semicontinuous and that the converse is true on a wide range of rearrangement invariant spaces. We also study inf-convolutions of law-invariant or surplus-invaria"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.05259","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":""},"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":"1805.05259","created_at":"2026-05-18T00:16:03.588493+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.05259v1","created_at":"2026-05-18T00:16:03.588493+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.05259","created_at":"2026-05-18T00:16:03.588493+00:00"},{"alias_kind":"pith_short_12","alias_value":"CLWNHXOL3NLU","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_16","alias_value":"CLWNHXOL3NLUGF5L","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_8","alias_value":"CLWNHXOL","created_at":"2026-05-18T12:32:16.446611+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/CLWNHXOL3NLUGF5LPZ3YW3LSIR","json":"https://pith.science/pith/CLWNHXOL3NLUGF5LPZ3YW3LSIR.json","graph_json":"https://pith.science/api/pith-number/CLWNHXOL3NLUGF5LPZ3YW3LSIR/graph.json","events_json":"https://pith.science/api/pith-number/CLWNHXOL3NLUGF5LPZ3YW3LSIR/events.json","paper":"https://pith.science/paper/CLWNHXOL"},"agent_actions":{"view_html":"https://pith.science/pith/CLWNHXOL3NLUGF5LPZ3YW3LSIR","download_json":"https://pith.science/pith/CLWNHXOL3NLUGF5LPZ3YW3LSIR.json","view_paper":"https://pith.science/paper/CLWNHXOL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.05259&json=true","fetch_graph":"https://pith.science/api/pith-number/CLWNHXOL3NLUGF5LPZ3YW3LSIR/graph.json","fetch_events":"https://pith.science/api/pith-number/CLWNHXOL3NLUGF5LPZ3YW3LSIR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CLWNHXOL3NLUGF5LPZ3YW3LSIR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CLWNHXOL3NLUGF5LPZ3YW3LSIR/action/storage_attestation","attest_author":"https://pith.science/pith/CLWNHXOL3NLUGF5LPZ3YW3LSIR/action/author_attestation","sign_citation":"https://pith.science/pith/CLWNHXOL3NLUGF5LPZ3YW3LSIR/action/citation_signature","submit_replication":"https://pith.science/pith/CLWNHXOL3NLUGF5LPZ3YW3LSIR/action/replication_record"}},"created_at":"2026-05-18T00:16:03.588493+00:00","updated_at":"2026-05-18T00:16:03.588493+00:00"}