{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:VBMT7WKJZW55HDZ2W3QSDLA73E","short_pith_number":"pith:VBMT7WKJ","schema_version":"1.0","canonical_sha256":"a8593fd949cdbbd38f3ab6e121ac1fd9321621d95bd315a306f4a65d35f6d549","source":{"kind":"arxiv","id":"1009.3479","version":2},"attestation_state":"computed","paper":{"title":"Incomplete Continuous-time Securities Markets with Stochastic Income Volatility","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-fin.GN","authors_text":"Kasper Larsen, Peter Ove Christensen","submitted_at":"2010-09-17T18:10:00Z","abstract_excerpt":"In an incomplete continuous-time securities market with uncertainty generated by Brownian motions, we derive closed-form solutions for the equilibrium interest rate and market price of risk processes. The economy has a finite number of heterogeneous exponential utility investors, who receive partially unspanned income and can trade continuously on a finite time-interval in a money market account and a single risky security. Besides establishing the existence of an equilibrium, our main result shows that if the investors' unspanned income has stochastic countercyclical volatility, the resulting"},"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":"1009.3479","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.GN","submitted_at":"2010-09-17T18:10:00Z","cross_cats_sorted":[],"title_canon_sha256":"fd7272bc9e6a1387b8b73d0e40e595d45506f47620b5fe6635ce42eee0b801e2","abstract_canon_sha256":"65af119be3601c6238a65fbd4b78524669c537174a79c484c657464ab7f4e47b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:15.125988Z","signature_b64":"ViGS1XfOKBPB6jlvFkptk2KWyDc2JjMARMi+2azjNAcFvmXEMA5SalWMg/eNrKjE9iAQn1hXEBtc1cJNZ9HxBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8593fd949cdbbd38f3ab6e121ac1fd9321621d95bd315a306f4a65d35f6d549","last_reissued_at":"2026-05-18T04:05:15.125523Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:15.125523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Incomplete Continuous-time Securities Markets with Stochastic Income Volatility","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-fin.GN","authors_text":"Kasper Larsen, Peter Ove Christensen","submitted_at":"2010-09-17T18:10:00Z","abstract_excerpt":"In an incomplete continuous-time securities market with uncertainty generated by Brownian motions, we derive closed-form solutions for the equilibrium interest rate and market price of risk processes. The economy has a finite number of heterogeneous exponential utility investors, who receive partially unspanned income and can trade continuously on a finite time-interval in a money market account and a single risky security. Besides establishing the existence of an equilibrium, our main result shows that if the investors' unspanned income has stochastic countercyclical volatility, the resulting"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3479","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":"1009.3479","created_at":"2026-05-18T04:05:15.125596+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.3479v2","created_at":"2026-05-18T04:05:15.125596+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3479","created_at":"2026-05-18T04:05:15.125596+00:00"},{"alias_kind":"pith_short_12","alias_value":"VBMT7WKJZW55","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_16","alias_value":"VBMT7WKJZW55HDZ2","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_8","alias_value":"VBMT7WKJ","created_at":"2026-05-18T12:26:15.391820+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/VBMT7WKJZW55HDZ2W3QSDLA73E","json":"https://pith.science/pith/VBMT7WKJZW55HDZ2W3QSDLA73E.json","graph_json":"https://pith.science/api/pith-number/VBMT7WKJZW55HDZ2W3QSDLA73E/graph.json","events_json":"https://pith.science/api/pith-number/VBMT7WKJZW55HDZ2W3QSDLA73E/events.json","paper":"https://pith.science/paper/VBMT7WKJ"},"agent_actions":{"view_html":"https://pith.science/pith/VBMT7WKJZW55HDZ2W3QSDLA73E","download_json":"https://pith.science/pith/VBMT7WKJZW55HDZ2W3QSDLA73E.json","view_paper":"https://pith.science/paper/VBMT7WKJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.3479&json=true","fetch_graph":"https://pith.science/api/pith-number/VBMT7WKJZW55HDZ2W3QSDLA73E/graph.json","fetch_events":"https://pith.science/api/pith-number/VBMT7WKJZW55HDZ2W3QSDLA73E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VBMT7WKJZW55HDZ2W3QSDLA73E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VBMT7WKJZW55HDZ2W3QSDLA73E/action/storage_attestation","attest_author":"https://pith.science/pith/VBMT7WKJZW55HDZ2W3QSDLA73E/action/author_attestation","sign_citation":"https://pith.science/pith/VBMT7WKJZW55HDZ2W3QSDLA73E/action/citation_signature","submit_replication":"https://pith.science/pith/VBMT7WKJZW55HDZ2W3QSDLA73E/action/replication_record"}},"created_at":"2026-05-18T04:05:15.125596+00:00","updated_at":"2026-05-18T04:05:15.125596+00:00"}