{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YEB6P74F7NSYK2B3LFWBST4D74","short_pith_number":"pith:YEB6P74F","canonical_record":{"source":{"id":"1309.0209","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-01T12:04:01Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"ef4e8684a95aef0bd5453198eabb6f317af0cbc7f8949a56ca98d96ac07bac2f","abstract_canon_sha256":"07067ae237e6c5e3ed2c3c7b701c7dad3f6d699f4aaa32dc158e24ec5c1636f9"},"schema_version":"1.0"},"canonical_sha256":"c103e7ff85fb6585683b596c194f83ff142b8222855b716d93ca5a915bf2fc63","source":{"kind":"arxiv","id":"1309.0209","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0209","created_at":"2026-05-18T03:14:28Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0209v1","created_at":"2026-05-18T03:14:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0209","created_at":"2026-05-18T03:14:28Z"},{"alias_kind":"pith_short_12","alias_value":"YEB6P74F7NSY","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YEB6P74F7NSYK2B3","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YEB6P74F","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YEB6P74F7NSYK2B3LFWBST4D74","target":"record","payload":{"canonical_record":{"source":{"id":"1309.0209","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-01T12:04:01Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"ef4e8684a95aef0bd5453198eabb6f317af0cbc7f8949a56ca98d96ac07bac2f","abstract_canon_sha256":"07067ae237e6c5e3ed2c3c7b701c7dad3f6d699f4aaa32dc158e24ec5c1636f9"},"schema_version":"1.0"},"canonical_sha256":"c103e7ff85fb6585683b596c194f83ff142b8222855b716d93ca5a915bf2fc63","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:28.587078Z","signature_b64":"fT5yoQaJ/H646gwAzG7nZOna7787MQ6qrv/tyB/KauJSwq4rRTfRS60hqb6xCRHW8VbxOs7dk4PrnOZjypKFCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c103e7ff85fb6585683b596c194f83ff142b8222855b716d93ca5a915bf2fc63","last_reissued_at":"2026-05-18T03:14:28.586420Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:28.586420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.0209","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":"2026-05-18T03:14:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kR0qoRSYw2uHLuicQGC6pVipEwluxEGLr6yAX+sue2W52q4M8nntcxPv/Gq7icLqV4s+6ZVIXvibI3cGyw9nBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T02:28:14.207031Z"},"content_sha256":"7fab76f763210ed599302c90215e2d288600b0f52e38a6a9d6952e98745d6d45","schema_version":"1.0","event_id":"sha256:7fab76f763210ed599302c90215e2d288600b0f52e38a6a9d6952e98745d6d45"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YEB6P74F7NSYK2B3LFWBST4D74","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal stochastic control and optimal consumption and portfolio with G-Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.OC","authors_text":"Chen Fei, Weiyin Fei","submitted_at":"2013-09-01T12:04:01Z","abstract_excerpt":"By the calculus of Peng's G-sublinear expectation and G-Brownian motion on a sublinear expectation space $(\\Omega, {\\cal H}, \\hat{\\mathbb{E}})$, we first set up an optimality principle of stochastic control problem. Then we investigate an optimal consumption and portfolio decision with a volatility ambiguity by the derived verification theorem. Next the two-fund separation theorem is explicitly obtained. And an illustrative example is provided."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0209","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":"2026-05-18T03:14:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IRWDvVbg57n6J2IB7XWMMqz7XIz54LrlOQ8ZhTKFDFmVAK5LkfnIjFSRGpDHU+9DUywdGhUPDVvqETpFKHXcAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T02:28:14.207398Z"},"content_sha256":"954726f9b75bed19ddc5f39984809ea1ab70dcdcfb8b225204dff4d87841571b","schema_version":"1.0","event_id":"sha256:954726f9b75bed19ddc5f39984809ea1ab70dcdcfb8b225204dff4d87841571b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YEB6P74F7NSYK2B3LFWBST4D74/bundle.json","state_url":"https://pith.science/pith/YEB6P74F7NSYK2B3LFWBST4D74/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YEB6P74F7NSYK2B3LFWBST4D74/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":"2026-06-21T02:28:14Z","links":{"resolver":"https://pith.science/pith/YEB6P74F7NSYK2B3LFWBST4D74","bundle":"https://pith.science/pith/YEB6P74F7NSYK2B3LFWBST4D74/bundle.json","state":"https://pith.science/pith/YEB6P74F7NSYK2B3LFWBST4D74/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YEB6P74F7NSYK2B3LFWBST4D74/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YEB6P74F7NSYK2B3LFWBST4D74","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":"07067ae237e6c5e3ed2c3c7b701c7dad3f6d699f4aaa32dc158e24ec5c1636f9","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-01T12:04:01Z","title_canon_sha256":"ef4e8684a95aef0bd5453198eabb6f317af0cbc7f8949a56ca98d96ac07bac2f"},"schema_version":"1.0","source":{"id":"1309.0209","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0209","created_at":"2026-05-18T03:14:28Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0209v1","created_at":"2026-05-18T03:14:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0209","created_at":"2026-05-18T03:14:28Z"},{"alias_kind":"pith_short_12","alias_value":"YEB6P74F7NSY","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YEB6P74F7NSYK2B3","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YEB6P74F","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:954726f9b75bed19ddc5f39984809ea1ab70dcdcfb8b225204dff4d87841571b","target":"graph","created_at":"2026-05-18T03:14:28Z","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":"By the calculus of Peng's G-sublinear expectation and G-Brownian motion on a sublinear expectation space $(\\Omega, {\\cal H}, \\hat{\\mathbb{E}})$, we first set up an optimality principle of stochastic control problem. Then we investigate an optimal consumption and portfolio decision with a volatility ambiguity by the derived verification theorem. Next the two-fund separation theorem is explicitly obtained. And an illustrative example is provided.","authors_text":"Chen Fei, Weiyin Fei","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-01T12:04:01Z","title":"Optimal stochastic control and optimal consumption and portfolio with G-Brownian motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0209","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":"sha256:7fab76f763210ed599302c90215e2d288600b0f52e38a6a9d6952e98745d6d45","target":"record","created_at":"2026-05-18T03:14:28Z","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":"07067ae237e6c5e3ed2c3c7b701c7dad3f6d699f4aaa32dc158e24ec5c1636f9","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-01T12:04:01Z","title_canon_sha256":"ef4e8684a95aef0bd5453198eabb6f317af0cbc7f8949a56ca98d96ac07bac2f"},"schema_version":"1.0","source":{"id":"1309.0209","kind":"arxiv","version":1}},"canonical_sha256":"c103e7ff85fb6585683b596c194f83ff142b8222855b716d93ca5a915bf2fc63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c103e7ff85fb6585683b596c194f83ff142b8222855b716d93ca5a915bf2fc63","first_computed_at":"2026-05-18T03:14:28.586420Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:28.586420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fT5yoQaJ/H646gwAzG7nZOna7787MQ6qrv/tyB/KauJSwq4rRTfRS60hqb6xCRHW8VbxOs7dk4PrnOZjypKFCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:28.587078Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.0209","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7fab76f763210ed599302c90215e2d288600b0f52e38a6a9d6952e98745d6d45","sha256:954726f9b75bed19ddc5f39984809ea1ab70dcdcfb8b225204dff4d87841571b"],"state_sha256":"884c0e0664b1dd6e8beb6debd37c2cdfb75174f80dc7e05a5f7ec7f131fdb322"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6D49vSXUqp/rEHHDGsSFAH31YZJD94ldvB6iF8B8YB6WI35lsyuWIp3YCPQzNyD0fOeb3O7N9gxxRk1ChTU0CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T02:28:14.209304Z","bundle_sha256":"40d9619bfd01e3abefc5e00515113cbe810c640c61c18b71715df745bc43c3df"}}