{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:2LNSUN2D222GN4NVAH645SUV3D","short_pith_number":"pith:2LNSUN2D","schema_version":"1.0","canonical_sha256":"d2db2a3743d6b466f1b501fdceca95d8d4aca5ffba93b63d45b69fa8ae24634d","source":{"kind":"arxiv","id":"1408.2709","version":1},"attestation_state":"computed","paper":{"title":"A Reduced Basis Method for Parabolic Partial Differential Equations with Parameter Functions and Application to Option Pricing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Antonia Mayerhofer, Karsten Urban","submitted_at":"2014-08-12T13:26:41Z","abstract_excerpt":"We consider the Heston model as an example of a parameterized parabolic partial differential equation. A space-time variational formulation is derived that allows for parameters in the coefficients (for calibration) as well as choosing the initial condition (for option pricing) as a parameter function. A corresponding discretization in space and time amd initial condition is introduced and shown to be stable. Finally, a Reduced Basis Method (RBM) is introduced that is able to use parameter functions also for the initial condition. Corresponding numerical results are shown."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1408.2709","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-08-12T13:26:41Z","cross_cats_sorted":[],"title_canon_sha256":"a1c31c4627b3a7b1c096a1974a340aeba26955ffa26ecae5eaa0696dce7ba56f","abstract_canon_sha256":"49a398a27d45283b53ef440411e7706264d93ad5abb5ec4ab636e77d65e9a1f6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:22.469803Z","signature_b64":"bV2ZJo17vtN96kvBPjH1WoXkLAQg82giIglkpcrZqvpaky1zjbCXQNRThauKI35Bs5NpVS6PmBFjhy+X9HQcBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2db2a3743d6b466f1b501fdceca95d8d4aca5ffba93b63d45b69fa8ae24634d","last_reissued_at":"2026-05-18T02:45:22.469382Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:22.469382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Reduced Basis Method for Parabolic Partial Differential Equations with Parameter Functions and Application to Option Pricing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Antonia Mayerhofer, Karsten Urban","submitted_at":"2014-08-12T13:26:41Z","abstract_excerpt":"We consider the Heston model as an example of a parameterized parabolic partial differential equation. A space-time variational formulation is derived that allows for parameters in the coefficients (for calibration) as well as choosing the initial condition (for option pricing) as a parameter function. A corresponding discretization in space and time amd initial condition is introduced and shown to be stable. Finally, a Reduced Basis Method (RBM) is introduced that is able to use parameter functions also for the initial condition. Corresponding numerical results are shown."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2709","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1408.2709","created_at":"2026-05-18T02:45:22.469440+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.2709v1","created_at":"2026-05-18T02:45:22.469440+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.2709","created_at":"2026-05-18T02:45:22.469440+00:00"},{"alias_kind":"pith_short_12","alias_value":"2LNSUN2D222G","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"2LNSUN2D222GN4NV","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"2LNSUN2D","created_at":"2026-05-18T12:28:11.866339+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2LNSUN2D222GN4NVAH645SUV3D","json":"https://pith.science/pith/2LNSUN2D222GN4NVAH645SUV3D.json","graph_json":"https://pith.science/api/pith-number/2LNSUN2D222GN4NVAH645SUV3D/graph.json","events_json":"https://pith.science/api/pith-number/2LNSUN2D222GN4NVAH645SUV3D/events.json","paper":"https://pith.science/paper/2LNSUN2D"},"agent_actions":{"view_html":"https://pith.science/pith/2LNSUN2D222GN4NVAH645SUV3D","download_json":"https://pith.science/pith/2LNSUN2D222GN4NVAH645SUV3D.json","view_paper":"https://pith.science/paper/2LNSUN2D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.2709&json=true","fetch_graph":"https://pith.science/api/pith-number/2LNSUN2D222GN4NVAH645SUV3D/graph.json","fetch_events":"https://pith.science/api/pith-number/2LNSUN2D222GN4NVAH645SUV3D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2LNSUN2D222GN4NVAH645SUV3D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2LNSUN2D222GN4NVAH645SUV3D/action/storage_attestation","attest_author":"https://pith.science/pith/2LNSUN2D222GN4NVAH645SUV3D/action/author_attestation","sign_citation":"https://pith.science/pith/2LNSUN2D222GN4NVAH645SUV3D/action/citation_signature","submit_replication":"https://pith.science/pith/2LNSUN2D222GN4NVAH645SUV3D/action/replication_record"}},"created_at":"2026-05-18T02:45:22.469440+00:00","updated_at":"2026-05-18T02:45:22.469440+00:00"}