{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ANQRH2A4LI3LDCVZPX2U6NYMPS","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":"0b7ce9f2ada226e11eeefae43a549bb3e4e8c7d844dd10d354d45c3ee0f17dd6","cross_cats_sorted":["q-fin.MF"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"q-fin.ST","submitted_at":"2016-05-03T19:15:33Z","title_canon_sha256":"8b566eed6ee5a8eb415fe370e037663d5295ff1d23d4ecb51e8ff8fd39c642e9"},"schema_version":"1.0","source":{"id":"1605.01028","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.01028","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"arxiv_version","alias_value":"1605.01028v1","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01028","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"pith_short_12","alias_value":"ANQRH2A4LI3L","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"ANQRH2A4LI3LDCVZ","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"ANQRH2A4","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:cc5b18eebf72c11f0d42439d806866acf067e7505b9a3bce879daf6cde98a5fa","target":"graph","created_at":"2026-05-18T01:15:47Z","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 pose an optimal control problem arising in a perhaps new model for retirement investing. Given a control function $f$ and our current net worth as $X(t)$ for any $t$, we invest an amount $f(X(t))$ in the market. We need a fortune of $M$ \"superdollars\" to retire and want to retire as early as possible. We model our change in net worth over each infinitesimal time interval by the Ito process $dX(t)= (1+f(X(t))dt+ f(X(t))dW(t)$. We show how to choose the optimal $f=f_0$ and show that the choice of $f_0$ is optimal among all nonanticipative investment strategies, not just among Markovian ones.","authors_text":"Dean Foster, Larry Shepp, Philip Ernst","cross_cats":["q-fin.MF"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"q-fin.ST","submitted_at":"2016-05-03T19:15:33Z","title":"On Optimal Retirement (How to Retire Early)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01028","kind":"arxiv","version":1},"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":"sha256:9ca785207a1b4a17484759ad738923bd363420fd1fef7cd85cad1cac2fce7242","target":"record","created_at":"2026-05-18T01:15:47Z","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":"0b7ce9f2ada226e11eeefae43a549bb3e4e8c7d844dd10d354d45c3ee0f17dd6","cross_cats_sorted":["q-fin.MF"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"q-fin.ST","submitted_at":"2016-05-03T19:15:33Z","title_canon_sha256":"8b566eed6ee5a8eb415fe370e037663d5295ff1d23d4ecb51e8ff8fd39c642e9"},"schema_version":"1.0","source":{"id":"1605.01028","kind":"arxiv","version":1}},"canonical_sha256":"036113e81c5a36b18ab97df54f370c7cb70e22009defb24596d05a95431f2fe1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"036113e81c5a36b18ab97df54f370c7cb70e22009defb24596d05a95431f2fe1","first_computed_at":"2026-05-18T01:15:47.450802Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:47.450802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lrpMoM1407bp3KY8m6vnE6y4PuKwt4qfr/QApE8GKvtFMrksQG+Ue2zg9I4A0BjBVS8BO3bFwwxQisG7D21rCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:47.451292Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.01028","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ca785207a1b4a17484759ad738923bd363420fd1fef7cd85cad1cac2fce7242","sha256:cc5b18eebf72c11f0d42439d806866acf067e7505b9a3bce879daf6cde98a5fa"],"state_sha256":"2250baf2933db75f9a9c273f45ed363f6392795aa89de733633b431c643cf54d"}