{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:PE4OQUU7HEWNEWIWJXBNBJ6JWH","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":"9d0b5932902b17a480e1acec3081a511b5f24cc44b0d64546f6e62bd298fe62f","cross_cats_sorted":["q-fin.CP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.RM","submitted_at":"2009-09-22T12:33:56Z","title_canon_sha256":"ac47986e87f078562166be9c0dc89f373e1cc39fb08a0064cc729a18e4fc60b8"},"schema_version":"1.0","source":{"id":"0909.3978","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.3978","created_at":"2026-05-18T03:56:22Z"},{"alias_kind":"arxiv_version","alias_value":"0909.3978v2","created_at":"2026-05-18T03:56:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.3978","created_at":"2026-05-18T03:56:22Z"},{"alias_kind":"pith_short_12","alias_value":"PE4OQUU7HEWN","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"PE4OQUU7HEWNEWIW","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"PE4OQUU7","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:6b7fe8e3c789a8ea9f3a09160c55cadd83b068a89b99949c6ffc9106edd97fc6","target":"graph","created_at":"2026-05-18T03:56:22Z","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 introduce the formalism of generalized Fourier transforms in the context of risk management. We develop a general framework to efficiently compute the most popular risk measures, Value-at-Risk and Expected Shortfall (also known as Conditional Value-at-Risk). The only ingredient required by our approach is the knowledge of the characteristic function describing the financial data in use. This allows to extend risk analysis to those non-Gaussian models defined in the Fourier space, such as Levy noise driven processes and stochastic volatility models. We test our analytical results on data set","authors_text":"G. Bormetti, G. Livan, G. Montagna, O. Nicrosini, V. Cazzola","cross_cats":["q-fin.CP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.RM","submitted_at":"2009-09-22T12:33:56Z","title":"A Generalized Fourier Transform Approach to Risk Measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.3978","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":"sha256:016cda1183e71caf9cae1590b0f6f8ce0fa0eba80251168991a39a05577e0c55","target":"record","created_at":"2026-05-18T03:56:22Z","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":"9d0b5932902b17a480e1acec3081a511b5f24cc44b0d64546f6e62bd298fe62f","cross_cats_sorted":["q-fin.CP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.RM","submitted_at":"2009-09-22T12:33:56Z","title_canon_sha256":"ac47986e87f078562166be9c0dc89f373e1cc39fb08a0064cc729a18e4fc60b8"},"schema_version":"1.0","source":{"id":"0909.3978","kind":"arxiv","version":2}},"canonical_sha256":"7938e8529f392cd259164dc2d0a7c9b1e2b7e520541b157ad32951f0ce5e9f34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7938e8529f392cd259164dc2d0a7c9b1e2b7e520541b157ad32951f0ce5e9f34","first_computed_at":"2026-05-18T03:56:22.976195Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:22.976195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IJIk7ERl04xGqBPgJ8pCp20+R50nKpMAvuuNMcmUNE/rREp0LEVIjBi2uNZE0U2h5HAPrOm05HQJCsP4zeO8Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:22.976969Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.3978","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:016cda1183e71caf9cae1590b0f6f8ce0fa0eba80251168991a39a05577e0c55","sha256:6b7fe8e3c789a8ea9f3a09160c55cadd83b068a89b99949c6ffc9106edd97fc6"],"state_sha256":"10dcde8f884f20fc8f527945b87a3930be5bcab7e387062628c6a2dc81fb99d0"}