{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:TMEEPO6WKIQE2DW2I6HFTYVN2T","short_pith_number":"pith:TMEEPO6W","schema_version":"1.0","canonical_sha256":"9b0847bbd652204d0eda478e59e2add4fca24642def1fdbb62f1e3523cf33a0c","source":{"kind":"arxiv","id":"1102.3928","version":2},"attestation_state":"computed","paper":{"title":"Integral representations of risk functions for basket derivatives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.RM"],"primary_cat":"math.OC","authors_text":"Micha{\\l} Barski","submitted_at":"2011-02-18T22:04:24Z","abstract_excerpt":"The risk minimizing problem $\\mathbf{E}[l((H-X_T^{x,\\pi})^{+})]\\overset{\\pi}{\\longrightarrow}\\min$ in the multidimensional Black-Scholes framework is studied. Specific formulas for the minimal risk function and the cost reduction function for basket derivatives are shown. Explicit integral representations for the risk functions for $l(x)=x$ and $l(x)=x^p$, with $p>1$ for digital, quantos, outperformance and spread options are derived."},"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":"1102.3928","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-02-18T22:04:24Z","cross_cats_sorted":["q-fin.RM"],"title_canon_sha256":"a285477e3226d69c15aa9ef9e828adc2696ceb5bb4711c7aed892894ba16f783","abstract_canon_sha256":"ae9b5cd68abd1d8c77b78c177b5b6b31c8f6514488f0ad9ee909573cbc49599c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:10.787344Z","signature_b64":"0dK15gf93rNGpXiPIN86vS0h60xWjc0IE13o7bhavH/O00BVTXcVIG0DEzTNAnKneHYpelvpMjEC39e4RuV9Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b0847bbd652204d0eda478e59e2add4fca24642def1fdbb62f1e3523cf33a0c","last_reissued_at":"2026-05-18T01:23:10.786893Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:10.786893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integral representations of risk functions for basket derivatives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.RM"],"primary_cat":"math.OC","authors_text":"Micha{\\l} Barski","submitted_at":"2011-02-18T22:04:24Z","abstract_excerpt":"The risk minimizing problem $\\mathbf{E}[l((H-X_T^{x,\\pi})^{+})]\\overset{\\pi}{\\longrightarrow}\\min$ in the multidimensional Black-Scholes framework is studied. Specific formulas for the minimal risk function and the cost reduction function for basket derivatives are shown. Explicit integral representations for the risk functions for $l(x)=x$ and $l(x)=x^p$, with $p>1$ for digital, quantos, outperformance and spread options are derived."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3928","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1102.3928","created_at":"2026-05-18T01:23:10.786956+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.3928v2","created_at":"2026-05-18T01:23:10.786956+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3928","created_at":"2026-05-18T01:23:10.786956+00:00"},{"alias_kind":"pith_short_12","alias_value":"TMEEPO6WKIQE","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"TMEEPO6WKIQE2DW2","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"TMEEPO6W","created_at":"2026-05-18T12:26:42.757692+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/TMEEPO6WKIQE2DW2I6HFTYVN2T","json":"https://pith.science/pith/TMEEPO6WKIQE2DW2I6HFTYVN2T.json","graph_json":"https://pith.science/api/pith-number/TMEEPO6WKIQE2DW2I6HFTYVN2T/graph.json","events_json":"https://pith.science/api/pith-number/TMEEPO6WKIQE2DW2I6HFTYVN2T/events.json","paper":"https://pith.science/paper/TMEEPO6W"},"agent_actions":{"view_html":"https://pith.science/pith/TMEEPO6WKIQE2DW2I6HFTYVN2T","download_json":"https://pith.science/pith/TMEEPO6WKIQE2DW2I6HFTYVN2T.json","view_paper":"https://pith.science/paper/TMEEPO6W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.3928&json=true","fetch_graph":"https://pith.science/api/pith-number/TMEEPO6WKIQE2DW2I6HFTYVN2T/graph.json","fetch_events":"https://pith.science/api/pith-number/TMEEPO6WKIQE2DW2I6HFTYVN2T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TMEEPO6WKIQE2DW2I6HFTYVN2T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TMEEPO6WKIQE2DW2I6HFTYVN2T/action/storage_attestation","attest_author":"https://pith.science/pith/TMEEPO6WKIQE2DW2I6HFTYVN2T/action/author_attestation","sign_citation":"https://pith.science/pith/TMEEPO6WKIQE2DW2I6HFTYVN2T/action/citation_signature","submit_replication":"https://pith.science/pith/TMEEPO6WKIQE2DW2I6HFTYVN2T/action/replication_record"}},"created_at":"2026-05-18T01:23:10.786956+00:00","updated_at":"2026-05-18T01:23:10.786956+00:00"}