{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:PISIDAGYV6PMI3YXXCRZSDGISI","short_pith_number":"pith:PISIDAGY","canonical_record":{"source":{"id":"1306.2014","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-09T12:48:27Z","cross_cats_sorted":[],"title_canon_sha256":"5e0312392b9326b8c62a14d6519746120d9b52773d4238216f8df9d0a4c56ed6","abstract_canon_sha256":"831f6ebb1f2c159058b75bdca60072b03493fe5256a7c713d2e59e0c2804d253"},"schema_version":"1.0"},"canonical_sha256":"7a248180d8af9ec46f17b8a3990cc89218a51d633df19781287d9af4220193d8","source":{"kind":"arxiv","id":"1306.2014","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.2014","created_at":"2026-05-18T01:19:55Z"},{"alias_kind":"arxiv_version","alias_value":"1306.2014v2","created_at":"2026-05-18T01:19:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.2014","created_at":"2026-05-18T01:19:55Z"},{"alias_kind":"pith_short_12","alias_value":"PISIDAGYV6PM","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PISIDAGYV6PMI3YX","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PISIDAGY","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:PISIDAGYV6PMI3YXXCRZSDGISI","target":"record","payload":{"canonical_record":{"source":{"id":"1306.2014","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-09T12:48:27Z","cross_cats_sorted":[],"title_canon_sha256":"5e0312392b9326b8c62a14d6519746120d9b52773d4238216f8df9d0a4c56ed6","abstract_canon_sha256":"831f6ebb1f2c159058b75bdca60072b03493fe5256a7c713d2e59e0c2804d253"},"schema_version":"1.0"},"canonical_sha256":"7a248180d8af9ec46f17b8a3990cc89218a51d633df19781287d9af4220193d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:55.798750Z","signature_b64":"0SwKCvpQ+BUOwLZNLjAO0K6gyMBkLD1iKTR8XGdMbhtColTmmIsocQVK8a5WOvJBNPvaFDQ3PgJIC06OBoedDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a248180d8af9ec46f17b8a3990cc89218a51d633df19781287d9af4220193d8","last_reissued_at":"2026-05-18T01:19:55.798295Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:55.798295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.2014","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":"2026-05-18T01:19:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WfYiAtcvV43aXsJFmOYVLCu95DZS+6zeEggR+ow7F1ZN0LAbLXQfl77G0rNRBJIbSAdO1xh5RChtHctvkCMWAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T14:08:24.060450Z"},"content_sha256":"f83f56d5a413feaa2d8361bb792fef255e6036f2c647bd13ac61499ab3040a1b","schema_version":"1.0","event_id":"sha256:f83f56d5a413feaa2d8361bb792fef255e6036f2c647bd13ac61499ab3040a1b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:PISIDAGYV6PMI3YXXCRZSDGISI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The early exercise premium representation for American options on multiply assets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andrzej Rozkosz, Tomasz Klimsiak","submitted_at":"2013-06-09T12:48:27Z","abstract_excerpt":"In the paper we consider the problem of valuation of American options written on dividend-paying assets whose price dynamics follow the classical multidimensional Black and Scholes model. We provide a general early exercise premium representation formula for options with payoff functions which are convex or satisfy mild regularity assumptions. Examples include index options, spread options, call on max options, put on min options, multiply strike options and power-product options. In the proof of the formula we exploit close connections between the optimal stopping problems associated with val"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2014","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":"2026-05-18T01:19:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wRtgsA596kAQWClNNep+tvWWd+I414ARvzK0hUD1TaUW1zzLwJPHaLHoeyAdnwJTPV8s5Lg208OlEbL8rHzsDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T14:08:24.060786Z"},"content_sha256":"d74ba48b5bf06d80f7f7b11c0bd1cce31e82540e15346e955057140096b60798","schema_version":"1.0","event_id":"sha256:d74ba48b5bf06d80f7f7b11c0bd1cce31e82540e15346e955057140096b60798"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PISIDAGYV6PMI3YXXCRZSDGISI/bundle.json","state_url":"https://pith.science/pith/PISIDAGYV6PMI3YXXCRZSDGISI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PISIDAGYV6PMI3YXXCRZSDGISI/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":"2026-06-27T14:08:24Z","links":{"resolver":"https://pith.science/pith/PISIDAGYV6PMI3YXXCRZSDGISI","bundle":"https://pith.science/pith/PISIDAGYV6PMI3YXXCRZSDGISI/bundle.json","state":"https://pith.science/pith/PISIDAGYV6PMI3YXXCRZSDGISI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PISIDAGYV6PMI3YXXCRZSDGISI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PISIDAGYV6PMI3YXXCRZSDGISI","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":"831f6ebb1f2c159058b75bdca60072b03493fe5256a7c713d2e59e0c2804d253","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-09T12:48:27Z","title_canon_sha256":"5e0312392b9326b8c62a14d6519746120d9b52773d4238216f8df9d0a4c56ed6"},"schema_version":"1.0","source":{"id":"1306.2014","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.2014","created_at":"2026-05-18T01:19:55Z"},{"alias_kind":"arxiv_version","alias_value":"1306.2014v2","created_at":"2026-05-18T01:19:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.2014","created_at":"2026-05-18T01:19:55Z"},{"alias_kind":"pith_short_12","alias_value":"PISIDAGYV6PM","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PISIDAGYV6PMI3YX","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PISIDAGY","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:d74ba48b5bf06d80f7f7b11c0bd1cce31e82540e15346e955057140096b60798","target":"graph","created_at":"2026-05-18T01:19:55Z","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 the paper we consider the problem of valuation of American options written on dividend-paying assets whose price dynamics follow the classical multidimensional Black and Scholes model. We provide a general early exercise premium representation formula for options with payoff functions which are convex or satisfy mild regularity assumptions. Examples include index options, spread options, call on max options, put on min options, multiply strike options and power-product options. In the proof of the formula we exploit close connections between the optimal stopping problems associated with val","authors_text":"Andrzej Rozkosz, Tomasz Klimsiak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-09T12:48:27Z","title":"The early exercise premium representation for American options on multiply assets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2014","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:f83f56d5a413feaa2d8361bb792fef255e6036f2c647bd13ac61499ab3040a1b","target":"record","created_at":"2026-05-18T01:19:55Z","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":"831f6ebb1f2c159058b75bdca60072b03493fe5256a7c713d2e59e0c2804d253","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-09T12:48:27Z","title_canon_sha256":"5e0312392b9326b8c62a14d6519746120d9b52773d4238216f8df9d0a4c56ed6"},"schema_version":"1.0","source":{"id":"1306.2014","kind":"arxiv","version":2}},"canonical_sha256":"7a248180d8af9ec46f17b8a3990cc89218a51d633df19781287d9af4220193d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a248180d8af9ec46f17b8a3990cc89218a51d633df19781287d9af4220193d8","first_computed_at":"2026-05-18T01:19:55.798295Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:55.798295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0SwKCvpQ+BUOwLZNLjAO0K6gyMBkLD1iKTR8XGdMbhtColTmmIsocQVK8a5WOvJBNPvaFDQ3PgJIC06OBoedDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:55.798750Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.2014","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f83f56d5a413feaa2d8361bb792fef255e6036f2c647bd13ac61499ab3040a1b","sha256:d74ba48b5bf06d80f7f7b11c0bd1cce31e82540e15346e955057140096b60798"],"state_sha256":"9890779b2da68c3047bc545f977e04479fdb8f67a150a23945ad929313e57628"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1XIBfn2HWBw2Zjl5H/FtIvp045RQBkq3POwfZekJYCW2lIkBa0UiIWoz7jyuz36dzRC1EP4aTnOFGiqEfZRFDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T14:08:24.062596Z","bundle_sha256":"a1282ce2f1a51fcccb51ffd02452ac22ce5e16149cfa4f3f7741196a2a41e22f"}}