{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NIJ6XWIHRPKEOXDR24G4FH77GH","short_pith_number":"pith:NIJ6XWIH","canonical_record":{"source":{"id":"1507.02974","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2015-07-10T17:41:38Z","cross_cats_sorted":[],"title_canon_sha256":"551253ace4b7d92ade26898322b04e3df2a4773e633c0977dbe34bfc986645dc","abstract_canon_sha256":"5e1bf992a23a37c0338c73b540fe2b9eaf9be68b48a45e22fbff2c728e5bfcab"},"schema_version":"1.0"},"canonical_sha256":"6a13ebd9078bd4475c71d70dc29fff31e8e3ff3fcb78474dd7bb2b19f16d2273","source":{"kind":"arxiv","id":"1507.02974","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02974","created_at":"2026-05-18T01:37:01Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02974v2","created_at":"2026-05-18T01:37:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02974","created_at":"2026-05-18T01:37:01Z"},{"alias_kind":"pith_short_12","alias_value":"NIJ6XWIHRPKE","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NIJ6XWIHRPKEOXDR","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NIJ6XWIH","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NIJ6XWIHRPKEOXDR24G4FH77GH","target":"record","payload":{"canonical_record":{"source":{"id":"1507.02974","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2015-07-10T17:41:38Z","cross_cats_sorted":[],"title_canon_sha256":"551253ace4b7d92ade26898322b04e3df2a4773e633c0977dbe34bfc986645dc","abstract_canon_sha256":"5e1bf992a23a37c0338c73b540fe2b9eaf9be68b48a45e22fbff2c728e5bfcab"},"schema_version":"1.0"},"canonical_sha256":"6a13ebd9078bd4475c71d70dc29fff31e8e3ff3fcb78474dd7bb2b19f16d2273","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:01.200565Z","signature_b64":"nInX81TQDze3hg1wqWFNfYtmreROlB1uGD5QtreWaoAr3wlOWjZN7XTMDpQrR0znyxDE1fXkRRSMdV+bx8NuBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a13ebd9078bd4475c71d70dc29fff31e8e3ff3fcb78474dd7bb2b19f16d2273","last_reissued_at":"2026-05-18T01:37:01.200027Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:01.200027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.02974","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:37:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SWGOmGZVKQUBTwWr4+SBMqil9Ol57+vTv88CThGqiMkxncvrIeX28sasYMJArAKlxrcbRVricDycCejpJ7MaDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T21:28:49.827654Z"},"content_sha256":"a0523c06cde86593f4d75fc93e6d06e5d82206c05fb952343a5f2dd8a5d619e8","schema_version":"1.0","event_id":"sha256:a0523c06cde86593f4d75fc93e6d06e5d82206c05fb952343a5f2dd8a5d619e8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NIJ6XWIHRPKEOXDR24G4FH77GH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Radner equilibrium in incomplete Levy models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-fin.MF","authors_text":"Kasper Larsen, Tanawit Sae Sue","submitted_at":"2015-07-10T17:41:38Z","abstract_excerpt":"We construct continuous-time equilibrium models based on a finite number of exponential utility investors. The investors' income rates as well as the stock's dividend rate are governed by discontinuous Levy processes. Our main result provides the equilibrium (i.e., bond and stock price dynamics) in closed-form. As an application, we show that the equilibrium Sharpe ratio can be increased and the equilibrium interest rate can be decreased (simultaneously) when the investors' income streams cannot be traded."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02974","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:37:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CLZ0HuGVn3Nn2VNK+HlGBXnXD41w4hEUvNfnxfvQJ8JY/RTn00Iusir5vv2o4aPoQIp/v/sStfdDEsOzWSN1Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T21:28:49.827976Z"},"content_sha256":"f5b22dd582b3f941be39640d39a63834ae8411c3333761e826605239fce21c05","schema_version":"1.0","event_id":"sha256:f5b22dd582b3f941be39640d39a63834ae8411c3333761e826605239fce21c05"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NIJ6XWIHRPKEOXDR24G4FH77GH/bundle.json","state_url":"https://pith.science/pith/NIJ6XWIHRPKEOXDR24G4FH77GH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NIJ6XWIHRPKEOXDR24G4FH77GH/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":"2026-06-27T21:28:49Z","links":{"resolver":"https://pith.science/pith/NIJ6XWIHRPKEOXDR24G4FH77GH","bundle":"https://pith.science/pith/NIJ6XWIHRPKEOXDR24G4FH77GH/bundle.json","state":"https://pith.science/pith/NIJ6XWIHRPKEOXDR24G4FH77GH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NIJ6XWIHRPKEOXDR24G4FH77GH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NIJ6XWIHRPKEOXDR24G4FH77GH","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":"5e1bf992a23a37c0338c73b540fe2b9eaf9be68b48a45e22fbff2c728e5bfcab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2015-07-10T17:41:38Z","title_canon_sha256":"551253ace4b7d92ade26898322b04e3df2a4773e633c0977dbe34bfc986645dc"},"schema_version":"1.0","source":{"id":"1507.02974","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02974","created_at":"2026-05-18T01:37:01Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02974v2","created_at":"2026-05-18T01:37:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02974","created_at":"2026-05-18T01:37:01Z"},{"alias_kind":"pith_short_12","alias_value":"NIJ6XWIHRPKE","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NIJ6XWIHRPKEOXDR","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NIJ6XWIH","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:f5b22dd582b3f941be39640d39a63834ae8411c3333761e826605239fce21c05","target":"graph","created_at":"2026-05-18T01:37:01Z","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 construct continuous-time equilibrium models based on a finite number of exponential utility investors. The investors' income rates as well as the stock's dividend rate are governed by discontinuous Levy processes. Our main result provides the equilibrium (i.e., bond and stock price dynamics) in closed-form. As an application, we show that the equilibrium Sharpe ratio can be increased and the equilibrium interest rate can be decreased (simultaneously) when the investors' income streams cannot be traded.","authors_text":"Kasper Larsen, Tanawit Sae Sue","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2015-07-10T17:41:38Z","title":"Radner equilibrium in incomplete Levy models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02974","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:a0523c06cde86593f4d75fc93e6d06e5d82206c05fb952343a5f2dd8a5d619e8","target":"record","created_at":"2026-05-18T01:37:01Z","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":"5e1bf992a23a37c0338c73b540fe2b9eaf9be68b48a45e22fbff2c728e5bfcab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2015-07-10T17:41:38Z","title_canon_sha256":"551253ace4b7d92ade26898322b04e3df2a4773e633c0977dbe34bfc986645dc"},"schema_version":"1.0","source":{"id":"1507.02974","kind":"arxiv","version":2}},"canonical_sha256":"6a13ebd9078bd4475c71d70dc29fff31e8e3ff3fcb78474dd7bb2b19f16d2273","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a13ebd9078bd4475c71d70dc29fff31e8e3ff3fcb78474dd7bb2b19f16d2273","first_computed_at":"2026-05-18T01:37:01.200027Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:01.200027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nInX81TQDze3hg1wqWFNfYtmreROlB1uGD5QtreWaoAr3wlOWjZN7XTMDpQrR0znyxDE1fXkRRSMdV+bx8NuBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:01.200565Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.02974","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0523c06cde86593f4d75fc93e6d06e5d82206c05fb952343a5f2dd8a5d619e8","sha256:f5b22dd582b3f941be39640d39a63834ae8411c3333761e826605239fce21c05"],"state_sha256":"786dd91aefb3cfd80b83f528d8fe25a45c6b4bb6896e5b41800b0ef76c976b7b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mRz+lITLyjg0kvNtkC9rWPylPAAm3+J2UDSIiwYkFkZ86b9nPtWF/b5hT6SURQJ+CZc89DS+kduLs+j05MUQCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T21:28:49.829706Z","bundle_sha256":"cf8b16044e0a6fcc313215e4fa7d78691a934e49f64bd799747531589bd08854"}}