{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ZCZIVLGE4VVHANUNLUKDHCCJ2W","short_pith_number":"pith:ZCZIVLGE","canonical_record":{"source":{"id":"1401.3921","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-16T07:41:39Z","cross_cats_sorted":["q-fin.PR"],"title_canon_sha256":"62ccf3326aab00b7a8c10d53504f0866befa40075546088d5a38abd538f7dba7","abstract_canon_sha256":"7532ffcda5cfedf240e8eb849140c712782191bbfe4617b0159c1abeea789dd7"},"schema_version":"1.0"},"canonical_sha256":"c8b28aacc4e56a70368d5d14338849d58a0a4ae8bee2a0b6e34bd2d7b3e666fb","source":{"kind":"arxiv","id":"1401.3921","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.3921","created_at":"2026-05-18T03:02:06Z"},{"alias_kind":"arxiv_version","alias_value":"1401.3921v1","created_at":"2026-05-18T03:02:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.3921","created_at":"2026-05-18T03:02:06Z"},{"alias_kind":"pith_short_12","alias_value":"ZCZIVLGE4VVH","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZCZIVLGE4VVHANUN","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZCZIVLGE","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ZCZIVLGE4VVHANUNLUKDHCCJ2W","target":"record","payload":{"canonical_record":{"source":{"id":"1401.3921","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-16T07:41:39Z","cross_cats_sorted":["q-fin.PR"],"title_canon_sha256":"62ccf3326aab00b7a8c10d53504f0866befa40075546088d5a38abd538f7dba7","abstract_canon_sha256":"7532ffcda5cfedf240e8eb849140c712782191bbfe4617b0159c1abeea789dd7"},"schema_version":"1.0"},"canonical_sha256":"c8b28aacc4e56a70368d5d14338849d58a0a4ae8bee2a0b6e34bd2d7b3e666fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:06.029870Z","signature_b64":"yn/vfGJsBNCYL0WnJ0z5HSsra6zWBoQGYw44YcP+SP7gTvV/ZDkC+sneZW8r10r8Xc5livn1ZkJt6eVpLID8Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8b28aacc4e56a70368d5d14338849d58a0a4ae8bee2a0b6e34bd2d7b3e666fb","last_reissued_at":"2026-05-18T03:02:06.029368Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:06.029368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.3921","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":"2026-05-18T03:02:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ECwNRCQC64R9rNfzFJ6npSQvnnM4VkqPjBJmh1SGHlB+NfbMD/eymhbStQK2GGXpjs6VIt10CqXF/7DOq1GuBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:58:36.430108Z"},"content_sha256":"aa68e4630afaf02ffa6eefe81ed7477b8c25ea0ea4b69dec4f6ac555883dab27","schema_version":"1.0","event_id":"sha256:aa68e4630afaf02ffa6eefe81ed7477b8c25ea0ea4b69dec4f6ac555883dab27"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ZCZIVLGE4VVHANUNLUKDHCCJ2W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.PR"],"primary_cat":"math.PR","authors_text":"A. Galichon, N. Touzi, P. Henry-Labord\\`ere","submitted_at":"2014-01-16T07:41:39Z","abstract_excerpt":"We consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset, and statically trade European call options for all possible strikes with some given maturity. This problem is classically approached by means of the Skorohod Embedding Problem (SEP). Instead, we provide a dual formulation which converts the superhedging problem into a continuous martingale optimal transportation problem. We then show that this formulation allows us to recover previously known results about lookback options. In particular, our methodology induc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.3921","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":"2026-05-18T03:02:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YZQYgU55BF8ZdqNWPTCzjgeKVAxrMajKQKGe0/TdqzCUs5zcAVVq1ktvIS0otCHj80R1I4mzg9nWqIt4g++nCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:58:36.431150Z"},"content_sha256":"5bf8f8644354c1526757916e8e7fa217506729fb1f2e5872212fd90cff433c85","schema_version":"1.0","event_id":"sha256:5bf8f8644354c1526757916e8e7fa217506729fb1f2e5872212fd90cff433c85"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZCZIVLGE4VVHANUNLUKDHCCJ2W/bundle.json","state_url":"https://pith.science/pith/ZCZIVLGE4VVHANUNLUKDHCCJ2W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZCZIVLGE4VVHANUNLUKDHCCJ2W/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":"2026-06-07T17:58:36Z","links":{"resolver":"https://pith.science/pith/ZCZIVLGE4VVHANUNLUKDHCCJ2W","bundle":"https://pith.science/pith/ZCZIVLGE4VVHANUNLUKDHCCJ2W/bundle.json","state":"https://pith.science/pith/ZCZIVLGE4VVHANUNLUKDHCCJ2W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZCZIVLGE4VVHANUNLUKDHCCJ2W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZCZIVLGE4VVHANUNLUKDHCCJ2W","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":"7532ffcda5cfedf240e8eb849140c712782191bbfe4617b0159c1abeea789dd7","cross_cats_sorted":["q-fin.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-16T07:41:39Z","title_canon_sha256":"62ccf3326aab00b7a8c10d53504f0866befa40075546088d5a38abd538f7dba7"},"schema_version":"1.0","source":{"id":"1401.3921","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.3921","created_at":"2026-05-18T03:02:06Z"},{"alias_kind":"arxiv_version","alias_value":"1401.3921v1","created_at":"2026-05-18T03:02:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.3921","created_at":"2026-05-18T03:02:06Z"},{"alias_kind":"pith_short_12","alias_value":"ZCZIVLGE4VVH","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZCZIVLGE4VVHANUN","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZCZIVLGE","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:5bf8f8644354c1526757916e8e7fa217506729fb1f2e5872212fd90cff433c85","target":"graph","created_at":"2026-05-18T03:02:06Z","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 consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset, and statically trade European call options for all possible strikes with some given maturity. This problem is classically approached by means of the Skorohod Embedding Problem (SEP). Instead, we provide a dual formulation which converts the superhedging problem into a continuous martingale optimal transportation problem. We then show that this formulation allows us to recover previously known results about lookback options. In particular, our methodology induc","authors_text":"A. Galichon, N. Touzi, P. Henry-Labord\\`ere","cross_cats":["q-fin.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-16T07:41:39Z","title":"A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.3921","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:aa68e4630afaf02ffa6eefe81ed7477b8c25ea0ea4b69dec4f6ac555883dab27","target":"record","created_at":"2026-05-18T03:02:06Z","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":"7532ffcda5cfedf240e8eb849140c712782191bbfe4617b0159c1abeea789dd7","cross_cats_sorted":["q-fin.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-16T07:41:39Z","title_canon_sha256":"62ccf3326aab00b7a8c10d53504f0866befa40075546088d5a38abd538f7dba7"},"schema_version":"1.0","source":{"id":"1401.3921","kind":"arxiv","version":1}},"canonical_sha256":"c8b28aacc4e56a70368d5d14338849d58a0a4ae8bee2a0b6e34bd2d7b3e666fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8b28aacc4e56a70368d5d14338849d58a0a4ae8bee2a0b6e34bd2d7b3e666fb","first_computed_at":"2026-05-18T03:02:06.029368Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:06.029368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yn/vfGJsBNCYL0WnJ0z5HSsra6zWBoQGYw44YcP+SP7gTvV/ZDkC+sneZW8r10r8Xc5livn1ZkJt6eVpLID8Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:06.029870Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.3921","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa68e4630afaf02ffa6eefe81ed7477b8c25ea0ea4b69dec4f6ac555883dab27","sha256:5bf8f8644354c1526757916e8e7fa217506729fb1f2e5872212fd90cff433c85"],"state_sha256":"df5cc600c2a2dbb5c1e565a1e68dcac76c4d1797017d7eec800bdc489a6d4d21"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iCSjdHQuDuEGuSrE8d5FCVt0/mDY0RSHDYGlVNXIZmu75VYcNnaxIrzcG6O5m4azZqE7gehb/un4wsz9yNwxBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T17:58:36.434947Z","bundle_sha256":"bf61608d7f81b007ff857fb71c2b006f7993219dc068b34159b525f14d0989bc"}}