{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:5RAJKPPJ2AUP55LY42S7K7Q7G6","short_pith_number":"pith:5RAJKPPJ","canonical_record":{"source":{"id":"1204.4852","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-22T02:59:19Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"91c416acda3e06d23692f3bc74eb7cfd0cd7c3d782cd15f57920dfbc9810c76e","abstract_canon_sha256":"79122a28cb71b0bddf53bff802788729c8105ac2fe9d3c51bd2d4f816f09dbc5"},"schema_version":"1.0"},"canonical_sha256":"ec40953de9d028fef578e6a5f57e1f37a8941c5e3e02b2c4853f91a655e1e42b","source":{"kind":"arxiv","id":"1204.4852","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.4852","created_at":"2026-05-18T03:38:12Z"},{"alias_kind":"arxiv_version","alias_value":"1204.4852v2","created_at":"2026-05-18T03:38:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.4852","created_at":"2026-05-18T03:38:12Z"},{"alias_kind":"pith_short_12","alias_value":"5RAJKPPJ2AUP","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"5RAJKPPJ2AUP55LY","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"5RAJKPPJ","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:5RAJKPPJ2AUP55LY42S7K7Q7G6","target":"record","payload":{"canonical_record":{"source":{"id":"1204.4852","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-22T02:59:19Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"91c416acda3e06d23692f3bc74eb7cfd0cd7c3d782cd15f57920dfbc9810c76e","abstract_canon_sha256":"79122a28cb71b0bddf53bff802788729c8105ac2fe9d3c51bd2d4f816f09dbc5"},"schema_version":"1.0"},"canonical_sha256":"ec40953de9d028fef578e6a5f57e1f37a8941c5e3e02b2c4853f91a655e1e42b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:12.586496Z","signature_b64":"7PH0ud1SBqE9e10mLOoO9Ky11npJ/2LOr/0WsY7/vZruU5rih5DAM6N5drBRUM5HJYSNNVSXVpkSAUXAFeg/Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec40953de9d028fef578e6a5f57e1f37a8941c5e3e02b2c4853f91a655e1e42b","last_reissued_at":"2026-05-18T03:38:12.586035Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:12.586035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.4852","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:38:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bxKjR/pDguOt/A67/ZYd9oIUpS5eNdw4cxRMx45GOXjxx3mj+TksPvWVaugj3N7bbVDdqsTQYRBZSbNPaEwuBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:09:51.920779Z"},"content_sha256":"10a34cee6f952e7cc3d230f25b56332ecf10b173c0f09237c627c795b422f664","schema_version":"1.0","event_id":"sha256:10a34cee6f952e7cc3d230f25b56332ecf10b173c0f09237c627c795b422f664"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:5RAJKPPJ2AUP55LY42S7K7Q7G6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Portfolio Selection under Concave Price Impact","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.PR","authors_text":"Jianfeng Zhang, Jing Xu, Jin Ma, Qingshuo Song","submitted_at":"2012-04-22T02:59:19Z","abstract_excerpt":"In this paper we study an optimal portfolio selection problem under instantaneous price impact. Based on some empirical analysis in the literature, we model such impact as a concave function of the trading size when the trading size is small. The price impact can be thought of as either a liquidity cost or a transaction cost, but the concavity nature of the cost leads to some fundamental difference from those in the existing literature. We show that the problem can be reduced to an impulse control problem, but without fixed cost, and that the value function is a viscosity solution to a special"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4852","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:38:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MEPiGXVVro7BFGBxZTFL3RFQo6ROMlKeKH1fvRywEe2yTE0rmn5VMUD0ib1kcPYIA7xJosZVsh/fIOuWhUEzAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:09:51.921517Z"},"content_sha256":"e5686c8a05ddb9fc6a5b9a5b21ba55dd460dba8e09873fc8b22cd0e4ca0688d2","schema_version":"1.0","event_id":"sha256:e5686c8a05ddb9fc6a5b9a5b21ba55dd460dba8e09873fc8b22cd0e4ca0688d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5RAJKPPJ2AUP55LY42S7K7Q7G6/bundle.json","state_url":"https://pith.science/pith/5RAJKPPJ2AUP55LY42S7K7Q7G6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5RAJKPPJ2AUP55LY42S7K7Q7G6/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":"2026-06-07T21:09:51Z","links":{"resolver":"https://pith.science/pith/5RAJKPPJ2AUP55LY42S7K7Q7G6","bundle":"https://pith.science/pith/5RAJKPPJ2AUP55LY42S7K7Q7G6/bundle.json","state":"https://pith.science/pith/5RAJKPPJ2AUP55LY42S7K7Q7G6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5RAJKPPJ2AUP55LY42S7K7Q7G6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5RAJKPPJ2AUP55LY42S7K7Q7G6","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":"79122a28cb71b0bddf53bff802788729c8105ac2fe9d3c51bd2d4f816f09dbc5","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-22T02:59:19Z","title_canon_sha256":"91c416acda3e06d23692f3bc74eb7cfd0cd7c3d782cd15f57920dfbc9810c76e"},"schema_version":"1.0","source":{"id":"1204.4852","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.4852","created_at":"2026-05-18T03:38:12Z"},{"alias_kind":"arxiv_version","alias_value":"1204.4852v2","created_at":"2026-05-18T03:38:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.4852","created_at":"2026-05-18T03:38:12Z"},{"alias_kind":"pith_short_12","alias_value":"5RAJKPPJ2AUP","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"5RAJKPPJ2AUP55LY","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"5RAJKPPJ","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:e5686c8a05ddb9fc6a5b9a5b21ba55dd460dba8e09873fc8b22cd0e4ca0688d2","target":"graph","created_at":"2026-05-18T03:38:12Z","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":"In this paper we study an optimal portfolio selection problem under instantaneous price impact. Based on some empirical analysis in the literature, we model such impact as a concave function of the trading size when the trading size is small. The price impact can be thought of as either a liquidity cost or a transaction cost, but the concavity nature of the cost leads to some fundamental difference from those in the existing literature. We show that the problem can be reduced to an impulse control problem, but without fixed cost, and that the value function is a viscosity solution to a special","authors_text":"Jianfeng Zhang, Jing Xu, Jin Ma, Qingshuo Song","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-22T02:59:19Z","title":"Optimal Portfolio Selection under Concave Price Impact"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4852","kind":"arxiv","version":2},"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":"sha256:10a34cee6f952e7cc3d230f25b56332ecf10b173c0f09237c627c795b422f664","target":"record","created_at":"2026-05-18T03:38:12Z","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":"79122a28cb71b0bddf53bff802788729c8105ac2fe9d3c51bd2d4f816f09dbc5","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-22T02:59:19Z","title_canon_sha256":"91c416acda3e06d23692f3bc74eb7cfd0cd7c3d782cd15f57920dfbc9810c76e"},"schema_version":"1.0","source":{"id":"1204.4852","kind":"arxiv","version":2}},"canonical_sha256":"ec40953de9d028fef578e6a5f57e1f37a8941c5e3e02b2c4853f91a655e1e42b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec40953de9d028fef578e6a5f57e1f37a8941c5e3e02b2c4853f91a655e1e42b","first_computed_at":"2026-05-18T03:38:12.586035Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:12.586035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7PH0ud1SBqE9e10mLOoO9Ky11npJ/2LOr/0WsY7/vZruU5rih5DAM6N5drBRUM5HJYSNNVSXVpkSAUXAFeg/Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:12.586496Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.4852","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10a34cee6f952e7cc3d230f25b56332ecf10b173c0f09237c627c795b422f664","sha256:e5686c8a05ddb9fc6a5b9a5b21ba55dd460dba8e09873fc8b22cd0e4ca0688d2"],"state_sha256":"feadf6b69db461fbc4c1adafe5f77dd5c82bca3df40547560a242cb820c90dc8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Asb5nEgDNLCWqJUdQ9RAizT/H4SUqbXBiID7j3wW8654+cAbLDB2cYcRygvnuonNQtMqwuCBG+pHkQjanYERDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T21:09:51.925668Z","bundle_sha256":"3fb924af3b15d0667f2ca0968adafc24295b66ff0adf6ab32c36711d8b2b10f5"}}