{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:TNYVC6Z2I2ISNIU75R77HUHOTJ","short_pith_number":"pith:TNYVC6Z2","canonical_record":{"source":{"id":"1107.0183","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-01T10:22:12Z","cross_cats_sorted":["q-fin.PM"],"title_canon_sha256":"df38352168cae216b19a913d2b2d9b2dd84e7302ee58867c8b588248f2172587","abstract_canon_sha256":"dab01ebfc179a0f99df1c68ffe5474841c834076c910733d475d942968bbab36"},"schema_version":"1.0"},"canonical_sha256":"9b71517b3a469126a29fec7ff3d0ee9a565f348b29636a6901593a65df764e83","source":{"kind":"arxiv","id":"1107.0183","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0183","created_at":"2026-05-18T03:56:08Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0183v2","created_at":"2026-05-18T03:56:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0183","created_at":"2026-05-18T03:56:08Z"},{"alias_kind":"pith_short_12","alias_value":"TNYVC6Z2I2IS","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TNYVC6Z2I2ISNIU7","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TNYVC6Z2","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:TNYVC6Z2I2ISNIU75R77HUHOTJ","target":"record","payload":{"canonical_record":{"source":{"id":"1107.0183","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-01T10:22:12Z","cross_cats_sorted":["q-fin.PM"],"title_canon_sha256":"df38352168cae216b19a913d2b2d9b2dd84e7302ee58867c8b588248f2172587","abstract_canon_sha256":"dab01ebfc179a0f99df1c68ffe5474841c834076c910733d475d942968bbab36"},"schema_version":"1.0"},"canonical_sha256":"9b71517b3a469126a29fec7ff3d0ee9a565f348b29636a6901593a65df764e83","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:08.594917Z","signature_b64":"aOQ+2KNXBJkxlLmwgbaBjdCqLBf9ZbNg4CtQWHhlb1QYzApy0x/LK/9/LCSOgJ7qvJsCUacx04+xn1uJxWESDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b71517b3a469126a29fec7ff3d0ee9a565f348b29636a6901593a65df764e83","last_reissued_at":"2026-05-18T03:56:08.594004Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:08.594004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.0183","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":"2026-05-18T03:56:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xgxzMVqlhdE0QWapKiy5vjPrnohIFpVMNaKW3AP0F/BFWQ22jV9MBTk+69RN4Ee3g6fTOVSIar6D+9QFBuaLAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:03:02.950154Z"},"content_sha256":"0eacca152e33f38e153114dc44cd229fd67dca79729cbfba0fea2863381d43b4","schema_version":"1.0","event_id":"sha256:0eacca152e33f38e153114dc44cd229fd67dca79729cbfba0fea2863381d43b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:TNYVC6Z2I2ISNIU75R77HUHOTJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"BSDEs in Utility Maximization with BMO Market Price of Risk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.PM"],"primary_cat":"math.PR","authors_text":"Christoph Frei, Markus Mocha, Nicholas Westray","submitted_at":"2011-07-01T10:22:12Z","abstract_excerpt":"This article studies quadratic semimartingale BSDEs arising in power utility maximization when the market price of risk is of BMO type. In a Brownian setting we provide a necessary and sufficient condition for the existence of a solution but show that uniqueness fails to hold in the sense that there exists a continuum of distinct square-integrable solutions. This feature occurs since, contrary to the classical Ito representation theorem, a representation of random variables in terms of stochastic exponentials is not unique. We study in detail when the BSDE has a bounded solution and derive a n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0183","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":"2026-05-18T03:56:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6p8TEdYFMLgpqz1QU0dsODUrWF2J0zs+RqUGlASHN1eXH5ipC0gREhvu51lPG2/tkwbKa+Z0a5cthSnznC4BAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:03:02.951026Z"},"content_sha256":"3ed50e93ac7319c19f51d7a2dd2bdc91876baad2a512c608738ab18c70f901ab","schema_version":"1.0","event_id":"sha256:3ed50e93ac7319c19f51d7a2dd2bdc91876baad2a512c608738ab18c70f901ab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TNYVC6Z2I2ISNIU75R77HUHOTJ/bundle.json","state_url":"https://pith.science/pith/TNYVC6Z2I2ISNIU75R77HUHOTJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TNYVC6Z2I2ISNIU75R77HUHOTJ/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":"2026-06-09T08:03:02Z","links":{"resolver":"https://pith.science/pith/TNYVC6Z2I2ISNIU75R77HUHOTJ","bundle":"https://pith.science/pith/TNYVC6Z2I2ISNIU75R77HUHOTJ/bundle.json","state":"https://pith.science/pith/TNYVC6Z2I2ISNIU75R77HUHOTJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TNYVC6Z2I2ISNIU75R77HUHOTJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TNYVC6Z2I2ISNIU75R77HUHOTJ","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":"dab01ebfc179a0f99df1c68ffe5474841c834076c910733d475d942968bbab36","cross_cats_sorted":["q-fin.PM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-01T10:22:12Z","title_canon_sha256":"df38352168cae216b19a913d2b2d9b2dd84e7302ee58867c8b588248f2172587"},"schema_version":"1.0","source":{"id":"1107.0183","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0183","created_at":"2026-05-18T03:56:08Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0183v2","created_at":"2026-05-18T03:56:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0183","created_at":"2026-05-18T03:56:08Z"},{"alias_kind":"pith_short_12","alias_value":"TNYVC6Z2I2IS","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TNYVC6Z2I2ISNIU7","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TNYVC6Z2","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:3ed50e93ac7319c19f51d7a2dd2bdc91876baad2a512c608738ab18c70f901ab","target":"graph","created_at":"2026-05-18T03:56:08Z","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":"This article studies quadratic semimartingale BSDEs arising in power utility maximization when the market price of risk is of BMO type. In a Brownian setting we provide a necessary and sufficient condition for the existence of a solution but show that uniqueness fails to hold in the sense that there exists a continuum of distinct square-integrable solutions. This feature occurs since, contrary to the classical Ito representation theorem, a representation of random variables in terms of stochastic exponentials is not unique. We study in detail when the BSDE has a bounded solution and derive a n","authors_text":"Christoph Frei, Markus Mocha, Nicholas Westray","cross_cats":["q-fin.PM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-01T10:22:12Z","title":"BSDEs in Utility Maximization with BMO Market Price of Risk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0183","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":"sha256:0eacca152e33f38e153114dc44cd229fd67dca79729cbfba0fea2863381d43b4","target":"record","created_at":"2026-05-18T03:56:08Z","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":"dab01ebfc179a0f99df1c68ffe5474841c834076c910733d475d942968bbab36","cross_cats_sorted":["q-fin.PM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-01T10:22:12Z","title_canon_sha256":"df38352168cae216b19a913d2b2d9b2dd84e7302ee58867c8b588248f2172587"},"schema_version":"1.0","source":{"id":"1107.0183","kind":"arxiv","version":2}},"canonical_sha256":"9b71517b3a469126a29fec7ff3d0ee9a565f348b29636a6901593a65df764e83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b71517b3a469126a29fec7ff3d0ee9a565f348b29636a6901593a65df764e83","first_computed_at":"2026-05-18T03:56:08.594004Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:08.594004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aOQ+2KNXBJkxlLmwgbaBjdCqLBf9ZbNg4CtQWHhlb1QYzApy0x/LK/9/LCSOgJ7qvJsCUacx04+xn1uJxWESDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:08.594917Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.0183","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0eacca152e33f38e153114dc44cd229fd67dca79729cbfba0fea2863381d43b4","sha256:3ed50e93ac7319c19f51d7a2dd2bdc91876baad2a512c608738ab18c70f901ab"],"state_sha256":"c66854e7e80f565f865b3b7a1a1c56cc04e5b1ba3c32531fc3911513e1d6a1ab"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZLqlnOFpaSirPHykin+baMmyFNvKNA0sS5rMZfB43Yfjhv5ElTU3eSEnmhOT2NxjBWLj4vrIZCTKtR6P4a8LBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T08:03:02.957875Z","bundle_sha256":"0e62814e9dc9a8eafa88e4af420ec5cd713dda81eae4f4a2773743da3c04c0fe"}}