{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:DT6VXIDFNF6I6MOAZ6B4JBVFVV","short_pith_number":"pith:DT6VXIDF","schema_version":"1.0","canonical_sha256":"1cfd5ba065697c8f31c0cf83c486a5ad45c8f37ab18c0a3a728a1d289fd2985e","source":{"kind":"arxiv","id":"1705.07472","version":1},"attestation_state":"computed","paper":{"title":"On the Black's equation for the risk tolerance function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-fin.PM","authors_text":"Sigrid K\\\"allblad, Thaleia Zariphopoulou","submitted_at":"2017-05-21T16:36:57Z","abstract_excerpt":"We analyze a nonlinear equation proposed by F. Black (1968) for the optimal portfolio function in a log-normal model. We cast it in terms of the risk tolerance function and provide, for general utility functions, existence, uniqueness and regularity results, and we also examine various monotonicity, concavity/convexity and S-shape properties. Stronger results are derived for utilities whose inverse marginal belongs to a class of completely monotonic functions."},"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":"1705.07472","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PM","submitted_at":"2017-05-21T16:36:57Z","cross_cats_sorted":[],"title_canon_sha256":"233267a3a975e3c70364e5b549becf97c4ea8fe14cedb35a0a3a9d4e22111dca","abstract_canon_sha256":"33b168fd131c14d39e638f19c97c531a57fa1300cf1dbfecd3061653d46f5901"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:05.487983Z","signature_b64":"vzh3A+gtTvTUdQkOjRPfiTJoUUJbm3VnOsFh+P+2q7F70kBQCqWe0uGplb1lIKZSxSee5o63wcKXPGfBP0KXBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cfd5ba065697c8f31c0cf83c486a5ad45c8f37ab18c0a3a728a1d289fd2985e","last_reissued_at":"2026-05-18T00:44:05.487280Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:05.487280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Black's equation for the risk tolerance function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-fin.PM","authors_text":"Sigrid K\\\"allblad, Thaleia Zariphopoulou","submitted_at":"2017-05-21T16:36:57Z","abstract_excerpt":"We analyze a nonlinear equation proposed by F. Black (1968) for the optimal portfolio function in a log-normal model. We cast it in terms of the risk tolerance function and provide, for general utility functions, existence, uniqueness and regularity results, and we also examine various monotonicity, concavity/convexity and S-shape properties. Stronger results are derived for utilities whose inverse marginal belongs to a class of completely monotonic functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07472","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":"1705.07472","created_at":"2026-05-18T00:44:05.487409+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.07472v1","created_at":"2026-05-18T00:44:05.487409+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.07472","created_at":"2026-05-18T00:44:05.487409+00:00"},{"alias_kind":"pith_short_12","alias_value":"DT6VXIDFNF6I","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"DT6VXIDFNF6I6MOA","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"DT6VXIDF","created_at":"2026-05-18T12:31:12.930513+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.14519","citing_title":"On the optimal portfolio problem with partial information and related mean field games with relative performance criteria","ref_index":35,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DT6VXIDFNF6I6MOAZ6B4JBVFVV","json":"https://pith.science/pith/DT6VXIDFNF6I6MOAZ6B4JBVFVV.json","graph_json":"https://pith.science/api/pith-number/DT6VXIDFNF6I6MOAZ6B4JBVFVV/graph.json","events_json":"https://pith.science/api/pith-number/DT6VXIDFNF6I6MOAZ6B4JBVFVV/events.json","paper":"https://pith.science/paper/DT6VXIDF"},"agent_actions":{"view_html":"https://pith.science/pith/DT6VXIDFNF6I6MOAZ6B4JBVFVV","download_json":"https://pith.science/pith/DT6VXIDFNF6I6MOAZ6B4JBVFVV.json","view_paper":"https://pith.science/paper/DT6VXIDF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.07472&json=true","fetch_graph":"https://pith.science/api/pith-number/DT6VXIDFNF6I6MOAZ6B4JBVFVV/graph.json","fetch_events":"https://pith.science/api/pith-number/DT6VXIDFNF6I6MOAZ6B4JBVFVV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DT6VXIDFNF6I6MOAZ6B4JBVFVV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DT6VXIDFNF6I6MOAZ6B4JBVFVV/action/storage_attestation","attest_author":"https://pith.science/pith/DT6VXIDFNF6I6MOAZ6B4JBVFVV/action/author_attestation","sign_citation":"https://pith.science/pith/DT6VXIDFNF6I6MOAZ6B4JBVFVV/action/citation_signature","submit_replication":"https://pith.science/pith/DT6VXIDFNF6I6MOAZ6B4JBVFVV/action/replication_record"}},"created_at":"2026-05-18T00:44:05.487409+00:00","updated_at":"2026-05-18T00:44:05.487409+00:00"}