{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:4F5IETMSVQHN7LYKSZDIN7K2MM","short_pith_number":"pith:4F5IETMS","canonical_record":{"source":{"id":"1111.6038","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2011-11-25T16:05:33Z","cross_cats_sorted":["math.PR","q-fin.PR"],"title_canon_sha256":"2ff600244c235a9f9648b835cf5aa246a63a10243f08f27a1400261358bfcf19","abstract_canon_sha256":"fbea8c6adabd58af61c85b71a31e4c8bab8731e0c83a8ec42379378010026b40"},"schema_version":"1.0"},"canonical_sha256":"e17a824d92ac0edfaf0a964686fd5a632ffa9c8d9d6cbc664fef0c15142860f8","source":{"kind":"arxiv","id":"1111.6038","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.6038","created_at":"2026-05-18T04:02:26Z"},{"alias_kind":"arxiv_version","alias_value":"1111.6038v2","created_at":"2026-05-18T04:02:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.6038","created_at":"2026-05-18T04:02:26Z"},{"alias_kind":"pith_short_12","alias_value":"4F5IETMSVQHN","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4F5IETMSVQHN7LYK","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4F5IETMS","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:4F5IETMSVQHN7LYKSZDIN7K2MM","target":"record","payload":{"canonical_record":{"source":{"id":"1111.6038","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2011-11-25T16:05:33Z","cross_cats_sorted":["math.PR","q-fin.PR"],"title_canon_sha256":"2ff600244c235a9f9648b835cf5aa246a63a10243f08f27a1400261358bfcf19","abstract_canon_sha256":"fbea8c6adabd58af61c85b71a31e4c8bab8731e0c83a8ec42379378010026b40"},"schema_version":"1.0"},"canonical_sha256":"e17a824d92ac0edfaf0a964686fd5a632ffa9c8d9d6cbc664fef0c15142860f8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:26.924282Z","signature_b64":"P+voF4t9AaIx/NI7x0eVFiWQ15NSsOOV1k6hphysZ9+wjLsmeBHakAD5hw/MYjh5QlZRCbswOOM9BisjscZeDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e17a824d92ac0edfaf0a964686fd5a632ffa9c8d9d6cbc664fef0c15142860f8","last_reissued_at":"2026-05-18T04:02:26.923811Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:26.923811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.6038","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":"2026-05-18T04:02:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rppgGHA1/JJn0YyxhgyyGE3rWE4jDbTzPhiJV2BkpB/d+WfD4XCH8Y71zVRxU+xnT/RQRO4Pa8yxcIuop1XRBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T13:09:11.223244Z"},"content_sha256":"4959c451d3e5ef8844826e1337756a2bec2b3319031e905d187a610df96c2fdf","schema_version":"1.0","event_id":"sha256:4959c451d3e5ef8844826e1337756a2bec2b3319031e905d187a610df96c2fdf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:4F5IETMSVQHN7LYKSZDIN7K2MM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal dual martingales, their analysis and application to new algorithms for Bermudan products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","q-fin.PR"],"primary_cat":"q-fin.CP","authors_text":"Jianing Zhang, John Schoenmakers, Junbo Huang","submitted_at":"2011-11-25T16:05:33Z","abstract_excerpt":"In this paper we introduce and study the concept of optimal and surely optimal dual martingales in the context of dual valuation of Bermudan options, and outline the development of new algorithms in this context. We provide a characterization theorem, a theorem which gives conditions for a martingale to be surely optimal, and a stability theorem concerning martingales which are near to be surely optimal in a sense. Guided by these results we develop a framework of backward algorithms for constructing such a martingale. In turn this martingale may then be utilized for computing an upper bound o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6038","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":"2026-05-18T04:02:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Am2+EsfQA/euGDT0g9EmmuMbQSY+bgXaskLhYkgTEcwyq+rhJ/s1BDvQRuHONJnnby3CxpoCrmjcrvmNPRVDAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T13:09:11.223878Z"},"content_sha256":"7e2149e8e18479a727cf75ff90b363ddf3c81ff2d6dcb1f1675665d31da89908","schema_version":"1.0","event_id":"sha256:7e2149e8e18479a727cf75ff90b363ddf3c81ff2d6dcb1f1675665d31da89908"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4F5IETMSVQHN7LYKSZDIN7K2MM/bundle.json","state_url":"https://pith.science/pith/4F5IETMSVQHN7LYKSZDIN7K2MM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4F5IETMSVQHN7LYKSZDIN7K2MM/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":"2026-06-03T13:09:11Z","links":{"resolver":"https://pith.science/pith/4F5IETMSVQHN7LYKSZDIN7K2MM","bundle":"https://pith.science/pith/4F5IETMSVQHN7LYKSZDIN7K2MM/bundle.json","state":"https://pith.science/pith/4F5IETMSVQHN7LYKSZDIN7K2MM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4F5IETMSVQHN7LYKSZDIN7K2MM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4F5IETMSVQHN7LYKSZDIN7K2MM","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":"fbea8c6adabd58af61c85b71a31e4c8bab8731e0c83a8ec42379378010026b40","cross_cats_sorted":["math.PR","q-fin.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2011-11-25T16:05:33Z","title_canon_sha256":"2ff600244c235a9f9648b835cf5aa246a63a10243f08f27a1400261358bfcf19"},"schema_version":"1.0","source":{"id":"1111.6038","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.6038","created_at":"2026-05-18T04:02:26Z"},{"alias_kind":"arxiv_version","alias_value":"1111.6038v2","created_at":"2026-05-18T04:02:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.6038","created_at":"2026-05-18T04:02:26Z"},{"alias_kind":"pith_short_12","alias_value":"4F5IETMSVQHN","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4F5IETMSVQHN7LYK","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4F5IETMS","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:7e2149e8e18479a727cf75ff90b363ddf3c81ff2d6dcb1f1675665d31da89908","target":"graph","created_at":"2026-05-18T04:02:26Z","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 introduce and study the concept of optimal and surely optimal dual martingales in the context of dual valuation of Bermudan options, and outline the development of new algorithms in this context. We provide a characterization theorem, a theorem which gives conditions for a martingale to be surely optimal, and a stability theorem concerning martingales which are near to be surely optimal in a sense. Guided by these results we develop a framework of backward algorithms for constructing such a martingale. In turn this martingale may then be utilized for computing an upper bound o","authors_text":"Jianing Zhang, John Schoenmakers, Junbo Huang","cross_cats":["math.PR","q-fin.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2011-11-25T16:05:33Z","title":"Optimal dual martingales, their analysis and application to new algorithms for Bermudan products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6038","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":"sha256:4959c451d3e5ef8844826e1337756a2bec2b3319031e905d187a610df96c2fdf","target":"record","created_at":"2026-05-18T04:02:26Z","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":"fbea8c6adabd58af61c85b71a31e4c8bab8731e0c83a8ec42379378010026b40","cross_cats_sorted":["math.PR","q-fin.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.CP","submitted_at":"2011-11-25T16:05:33Z","title_canon_sha256":"2ff600244c235a9f9648b835cf5aa246a63a10243f08f27a1400261358bfcf19"},"schema_version":"1.0","source":{"id":"1111.6038","kind":"arxiv","version":2}},"canonical_sha256":"e17a824d92ac0edfaf0a964686fd5a632ffa9c8d9d6cbc664fef0c15142860f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e17a824d92ac0edfaf0a964686fd5a632ffa9c8d9d6cbc664fef0c15142860f8","first_computed_at":"2026-05-18T04:02:26.923811Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:26.923811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P+voF4t9AaIx/NI7x0eVFiWQ15NSsOOV1k6hphysZ9+wjLsmeBHakAD5hw/MYjh5QlZRCbswOOM9BisjscZeDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:26.924282Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.6038","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4959c451d3e5ef8844826e1337756a2bec2b3319031e905d187a610df96c2fdf","sha256:7e2149e8e18479a727cf75ff90b363ddf3c81ff2d6dcb1f1675665d31da89908"],"state_sha256":"640efdbb6575d9be6fd321b9cd19280cff391ab649152248b946ec0fde4e7c56"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8EmKk7oEk4i3OAoyRfCDq4n9gGd/Jqzj6dJgNcty/dFvtHGRwBoTTjS3iEWIz/Nmf4tTBOcp1TUShJRolr6/Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T13:09:11.227249Z","bundle_sha256":"2a7edfac57729840fc6769b434e442ccb8f47995809fb30ce431807b6f87d5ab"}}