{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:FTC7XXGFUAEAERNCLTSL4VYSKU","short_pith_number":"pith:FTC7XXGF","canonical_record":{"source":{"id":"1707.01436","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2017-07-04T03:23:46Z","cross_cats_sorted":[],"title_canon_sha256":"7a668a441e7f07be0aef97ca56118dcaaba48b2b0c919f975d6f4c0651a7bfcb","abstract_canon_sha256":"509ba58f0eab728c8e37f1f0f50274e491a4255312643972776d10ea6cfc19c1"},"schema_version":"1.0"},"canonical_sha256":"2cc5fbdcc5a0080245a25ce4be571255041ad5d5da5d3de3c5b471818fffbce1","source":{"kind":"arxiv","id":"1707.01436","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.01436","created_at":"2026-05-18T00:40:52Z"},{"alias_kind":"arxiv_version","alias_value":"1707.01436v1","created_at":"2026-05-18T00:40:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01436","created_at":"2026-05-18T00:40:52Z"},{"alias_kind":"pith_short_12","alias_value":"FTC7XXGFUAEA","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FTC7XXGFUAEAERNC","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FTC7XXGF","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:FTC7XXGFUAEAERNCLTSL4VYSKU","target":"record","payload":{"canonical_record":{"source":{"id":"1707.01436","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2017-07-04T03:23:46Z","cross_cats_sorted":[],"title_canon_sha256":"7a668a441e7f07be0aef97ca56118dcaaba48b2b0c919f975d6f4c0651a7bfcb","abstract_canon_sha256":"509ba58f0eab728c8e37f1f0f50274e491a4255312643972776d10ea6cfc19c1"},"schema_version":"1.0"},"canonical_sha256":"2cc5fbdcc5a0080245a25ce4be571255041ad5d5da5d3de3c5b471818fffbce1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:52.307621Z","signature_b64":"WKNunXjFGbWlHRdke3kOildBj/QKrIPm98nDaVaJnZIurmrcnt/1SKkyUigpsiWQMbDZvntuXnuzsKswBVd7CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2cc5fbdcc5a0080245a25ce4be571255041ad5d5da5d3de3c5b471818fffbce1","last_reissued_at":"2026-05-18T00:40:52.306896Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:52.306896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.01436","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":"2026-05-18T00:40:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SOysAe0vZPI0LCU6s/1bChBISa8CvM7ctusSiTCjDbYUWTaQ/mRzctZRxbHreLCPbdMAM+H9g0IhYDNPUI0bBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T01:32:40.331169Z"},"content_sha256":"142d144bb0ef4e4c43ab55b48ed24e8264d7e0723ba10a62c86c81c57088b3eb","schema_version":"1.0","event_id":"sha256:142d144bb0ef4e4c43ab55b48ed24e8264d7e0723ba10a62c86c81c57088b3eb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:FTC7XXGFUAEAERNCLTSL4VYSKU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinear Parabolic Equations arising in Mathematical Finance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-fin.PR","authors_text":"Daniel Sevcovic","submitted_at":"2017-07-04T03:23:46Z","abstract_excerpt":"This survey paper is focused on qualitative and numerical analyses of fully nonlinear partial differential equations of parabolic type arising in financial mathematics. The main purpose is to review various non-linear extensions of the classical Black-Scholes theory for pricing financial instruments, as well as models of stochastic dynamic portfolio optimization leading to the Hamilton-Jacobi-Bellman (HJB) equation. After suitable transformations, both problems can be represented by solutions to nonlinear parabolic equations. Qualitative analysis will be focused on issues concerning the existe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01436","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":"2026-05-18T00:40:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hmdtte3Co3PRQ8rHy+5/sOVR1GZg+0JfjtC250xtOxfgB0/Uw4VMnoNYH8CTX/MYhtw3Oo59egUpfWi8an+8AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T01:32:40.331521Z"},"content_sha256":"67554fb66edb0f4407fe15d13d057c9f8d95f2f980c36ed1fa6e16cbdd30198c","schema_version":"1.0","event_id":"sha256:67554fb66edb0f4407fe15d13d057c9f8d95f2f980c36ed1fa6e16cbdd30198c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FTC7XXGFUAEAERNCLTSL4VYSKU/bundle.json","state_url":"https://pith.science/pith/FTC7XXGFUAEAERNCLTSL4VYSKU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FTC7XXGFUAEAERNCLTSL4VYSKU/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":"2026-06-26T01:32:40Z","links":{"resolver":"https://pith.science/pith/FTC7XXGFUAEAERNCLTSL4VYSKU","bundle":"https://pith.science/pith/FTC7XXGFUAEAERNCLTSL4VYSKU/bundle.json","state":"https://pith.science/pith/FTC7XXGFUAEAERNCLTSL4VYSKU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FTC7XXGFUAEAERNCLTSL4VYSKU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FTC7XXGFUAEAERNCLTSL4VYSKU","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":"509ba58f0eab728c8e37f1f0f50274e491a4255312643972776d10ea6cfc19c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2017-07-04T03:23:46Z","title_canon_sha256":"7a668a441e7f07be0aef97ca56118dcaaba48b2b0c919f975d6f4c0651a7bfcb"},"schema_version":"1.0","source":{"id":"1707.01436","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.01436","created_at":"2026-05-18T00:40:52Z"},{"alias_kind":"arxiv_version","alias_value":"1707.01436v1","created_at":"2026-05-18T00:40:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01436","created_at":"2026-05-18T00:40:52Z"},{"alias_kind":"pith_short_12","alias_value":"FTC7XXGFUAEA","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FTC7XXGFUAEAERNC","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FTC7XXGF","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:67554fb66edb0f4407fe15d13d057c9f8d95f2f980c36ed1fa6e16cbdd30198c","target":"graph","created_at":"2026-05-18T00:40:52Z","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 survey paper is focused on qualitative and numerical analyses of fully nonlinear partial differential equations of parabolic type arising in financial mathematics. The main purpose is to review various non-linear extensions of the classical Black-Scholes theory for pricing financial instruments, as well as models of stochastic dynamic portfolio optimization leading to the Hamilton-Jacobi-Bellman (HJB) equation. After suitable transformations, both problems can be represented by solutions to nonlinear parabolic equations. Qualitative analysis will be focused on issues concerning the existe","authors_text":"Daniel Sevcovic","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2017-07-04T03:23:46Z","title":"Nonlinear Parabolic Equations arising in Mathematical Finance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01436","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":"sha256:142d144bb0ef4e4c43ab55b48ed24e8264d7e0723ba10a62c86c81c57088b3eb","target":"record","created_at":"2026-05-18T00:40:52Z","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":"509ba58f0eab728c8e37f1f0f50274e491a4255312643972776d10ea6cfc19c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2017-07-04T03:23:46Z","title_canon_sha256":"7a668a441e7f07be0aef97ca56118dcaaba48b2b0c919f975d6f4c0651a7bfcb"},"schema_version":"1.0","source":{"id":"1707.01436","kind":"arxiv","version":1}},"canonical_sha256":"2cc5fbdcc5a0080245a25ce4be571255041ad5d5da5d3de3c5b471818fffbce1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2cc5fbdcc5a0080245a25ce4be571255041ad5d5da5d3de3c5b471818fffbce1","first_computed_at":"2026-05-18T00:40:52.306896Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:52.306896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WKNunXjFGbWlHRdke3kOildBj/QKrIPm98nDaVaJnZIurmrcnt/1SKkyUigpsiWQMbDZvntuXnuzsKswBVd7CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:52.307621Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.01436","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:142d144bb0ef4e4c43ab55b48ed24e8264d7e0723ba10a62c86c81c57088b3eb","sha256:67554fb66edb0f4407fe15d13d057c9f8d95f2f980c36ed1fa6e16cbdd30198c"],"state_sha256":"f60d4f71b999db47a0c8ed5e336763f783e010e71f0b4bf6b38c8fb0d0731bcc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KIpzpKg1Bhz6TasMDRuRdnFXeM9B7fcxCIROZRpKPEM9j7FPyRzooNRwh61u0Jnf/E//JmdQGKeoCJkdNyY1BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T01:32:40.333302Z","bundle_sha256":"690cf7fb1fd8ced418ac49c0235f8e1138a7f006083ed63b503a0486822297c4"}}