{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:2T5YQGN3VYZYD7NO7BDDJREM2Y","short_pith_number":"pith:2T5YQGN3","canonical_record":{"source":{"id":"1811.06893","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PM","submitted_at":"2018-11-16T16:30:19Z","cross_cats_sorted":["math.OC","q-fin.CP"],"title_canon_sha256":"c9137c5663fd787de80e32fa00d235b0dcb16505a81b837521f1312213a24980","abstract_canon_sha256":"b31003313f4e08f94105648882fe724d730eab2a13ec33c7fb267fd7f55aeb7f"},"schema_version":"1.0"},"canonical_sha256":"d4fb8819bbae3381fdaef84634c48cd6207f4785db5d4e5e7043f7b493d66042","source":{"kind":"arxiv","id":"1811.06893","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.06893","created_at":"2026-05-18T00:00:33Z"},{"alias_kind":"arxiv_version","alias_value":"1811.06893v1","created_at":"2026-05-18T00:00:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.06893","created_at":"2026-05-18T00:00:33Z"},{"alias_kind":"pith_short_12","alias_value":"2T5YQGN3VYZY","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2T5YQGN3VYZYD7NO","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2T5YQGN3","created_at":"2026-05-18T12:32:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:2T5YQGN3VYZYD7NO7BDDJREM2Y","target":"record","payload":{"canonical_record":{"source":{"id":"1811.06893","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PM","submitted_at":"2018-11-16T16:30:19Z","cross_cats_sorted":["math.OC","q-fin.CP"],"title_canon_sha256":"c9137c5663fd787de80e32fa00d235b0dcb16505a81b837521f1312213a24980","abstract_canon_sha256":"b31003313f4e08f94105648882fe724d730eab2a13ec33c7fb267fd7f55aeb7f"},"schema_version":"1.0"},"canonical_sha256":"d4fb8819bbae3381fdaef84634c48cd6207f4785db5d4e5e7043f7b493d66042","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:33.547274Z","signature_b64":"663z0tejifYHh5VUH7SWk3uC6YgbADMC7rRseMl4h/d7O/ks67fL7UK9G2yMa/As6O6/7GxkLSVIHQGevSZlAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4fb8819bbae3381fdaef84634c48cd6207f4785db5d4e5e7043f7b493d66042","last_reissued_at":"2026-05-18T00:00:33.546823Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:33.546823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.06893","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:00:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VKCAlIYskeTiukzvUVnPZS3JSB6IY3o946or36e+7wisgGq3XcqlWygy9279qGL7AeJ+Gmr5waPt57DS0KAGDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:41:26.040648Z"},"content_sha256":"6b9b04d164def77ce70991aecf64a2af8e07694399fc60118de362a3b930adc0","schema_version":"1.0","event_id":"sha256:6b9b04d164def77ce70991aecf64a2af8e07694399fc60118de362a3b930adc0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:2T5YQGN3VYZYD7NO7BDDJREM2Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bayesian learning for the Markowitz portfolio selection problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","q-fin.CP"],"primary_cat":"q-fin.PM","authors_text":"Carmine De Franco, CREST), Huy\\^en Pham (LPSM UMR 8001, Johann Nicolle (LPSM UMR 8001)","submitted_at":"2018-11-16T16:30:19Z","abstract_excerpt":"We study  the Markowitz portfolio selection problem with unknown drift vector in the multidimensional framework. The prior belief on the uncertain expected rate of return is modeled by an arbitrary  probability law, and a Bayesian approach from filtering theory is used to learn the posterior distribution about the drift given the observed market data of the assets. The Bayesian Markowitz problem is then embedded into an auxiliary standard control problem that we characterize by a dynamic programming method and prove the existence and uniqueness of a smooth solution to the related semi-linear p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.06893","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:00:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IG/iKvIQY+aXCGgXuGjiPfuuykV200q3Oe7nJxcwhyLRX8kzHBkT744A+GFk7i6K0T0n6vc7QGwvMmkdriRGCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:41:26.041001Z"},"content_sha256":"09536d48443772bf16ef58bea649f026cf641f06475ac356b0134686fbe02f53","schema_version":"1.0","event_id":"sha256:09536d48443772bf16ef58bea649f026cf641f06475ac356b0134686fbe02f53"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2T5YQGN3VYZYD7NO7BDDJREM2Y/bundle.json","state_url":"https://pith.science/pith/2T5YQGN3VYZYD7NO7BDDJREM2Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2T5YQGN3VYZYD7NO7BDDJREM2Y/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T07:41:26Z","links":{"resolver":"https://pith.science/pith/2T5YQGN3VYZYD7NO7BDDJREM2Y","bundle":"https://pith.science/pith/2T5YQGN3VYZYD7NO7BDDJREM2Y/bundle.json","state":"https://pith.science/pith/2T5YQGN3VYZYD7NO7BDDJREM2Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2T5YQGN3VYZYD7NO7BDDJREM2Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2T5YQGN3VYZYD7NO7BDDJREM2Y","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b31003313f4e08f94105648882fe724d730eab2a13ec33c7fb267fd7f55aeb7f","cross_cats_sorted":["math.OC","q-fin.CP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PM","submitted_at":"2018-11-16T16:30:19Z","title_canon_sha256":"c9137c5663fd787de80e32fa00d235b0dcb16505a81b837521f1312213a24980"},"schema_version":"1.0","source":{"id":"1811.06893","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.06893","created_at":"2026-05-18T00:00:33Z"},{"alias_kind":"arxiv_version","alias_value":"1811.06893v1","created_at":"2026-05-18T00:00:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.06893","created_at":"2026-05-18T00:00:33Z"},{"alias_kind":"pith_short_12","alias_value":"2T5YQGN3VYZY","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2T5YQGN3VYZYD7NO","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2T5YQGN3","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:09536d48443772bf16ef58bea649f026cf641f06475ac356b0134686fbe02f53","target":"graph","created_at":"2026-05-18T00:00:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study  the Markowitz portfolio selection problem with unknown drift vector in the multidimensional framework. The prior belief on the uncertain expected rate of return is modeled by an arbitrary  probability law, and a Bayesian approach from filtering theory is used to learn the posterior distribution about the drift given the observed market data of the assets. The Bayesian Markowitz problem is then embedded into an auxiliary standard control problem that we characterize by a dynamic programming method and prove the existence and uniqueness of a smooth solution to the related semi-linear p","authors_text":"Carmine De Franco, CREST), Huy\\^en Pham (LPSM UMR 8001, Johann Nicolle (LPSM UMR 8001)","cross_cats":["math.OC","q-fin.CP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PM","submitted_at":"2018-11-16T16:30:19Z","title":"Bayesian learning for the Markowitz portfolio selection problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.06893","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6b9b04d164def77ce70991aecf64a2af8e07694399fc60118de362a3b930adc0","target":"record","created_at":"2026-05-18T00:00:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b31003313f4e08f94105648882fe724d730eab2a13ec33c7fb267fd7f55aeb7f","cross_cats_sorted":["math.OC","q-fin.CP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PM","submitted_at":"2018-11-16T16:30:19Z","title_canon_sha256":"c9137c5663fd787de80e32fa00d235b0dcb16505a81b837521f1312213a24980"},"schema_version":"1.0","source":{"id":"1811.06893","kind":"arxiv","version":1}},"canonical_sha256":"d4fb8819bbae3381fdaef84634c48cd6207f4785db5d4e5e7043f7b493d66042","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4fb8819bbae3381fdaef84634c48cd6207f4785db5d4e5e7043f7b493d66042","first_computed_at":"2026-05-18T00:00:33.546823Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:33.546823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"663z0tejifYHh5VUH7SWk3uC6YgbADMC7rRseMl4h/d7O/ks67fL7UK9G2yMa/As6O6/7GxkLSVIHQGevSZlAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:33.547274Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.06893","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b9b04d164def77ce70991aecf64a2af8e07694399fc60118de362a3b930adc0","sha256:09536d48443772bf16ef58bea649f026cf641f06475ac356b0134686fbe02f53"],"state_sha256":"8c12b63f6e66e12653271bc8666e1d9895f54ecf15858dcfde7d73e7db69ab3b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LO3eMTawn94wN3NKXrNzLa0/mrgtfLP3Bh1R4uZaiuD2XIgQmZONyYaMrIoWDbtTji9z5J3IfAlBFtIGWRb+Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T07:41:26.042986Z","bundle_sha256":"c057caf43ce6deff5cdce62bf2c7bde20a3f508d9573809ec55ea7d6f9a17365"}}