{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7LQU3G5BQGKYSG2NY53FW73LID","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":"a8cc46f484092222696caba607ccf22d2e8d5954071aa945a903f1518d811b33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-06T17:19:24Z","title_canon_sha256":"d5982acbd0d1f141ad59d6d3c6e923f715e68d2469f24f16d07a8291b1a788af"},"schema_version":"1.0","source":{"id":"1505.01437","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.01437","created_at":"2026-05-18T01:30:42Z"},{"alias_kind":"arxiv_version","alias_value":"1505.01437v2","created_at":"2026-05-18T01:30:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.01437","created_at":"2026-05-18T01:30:42Z"},{"alias_kind":"pith_short_12","alias_value":"7LQU3G5BQGKY","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7LQU3G5BQGKYSG2N","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7LQU3G5B","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:184a28e9db6e8c67a97a402aa7183f4a7263e28596d73f7e68b8c2b6b09b7dca","target":"graph","created_at":"2026-05-18T01:30:42Z","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":"Following the paper by Algoet--Cover (1988), we analyse log-optimal portfolios where return evaluation includes `weights' of different outcomes. The results are twofold: (A) under certain conditions, logarithmic growth rate is a supermartingale, and (B) the optimal (martingale) investment strategy is a proportional betting; it does not depend on the form of the weight function, although the optimal rate does. The existence of an optimal investment strategy has been established earlier in a great generality by Kramkov--Schachermayer (2003) although our underlying assumptions are different.","authors_text":"I. Stuhl, M. Kelbert, Y. Suhov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-06T17:19:24Z","title":"Weight functions and log-optimal investment portfolios"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01437","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:fbe1e1fbff34279a2205da4a8bc3e02949cc08ef9176e71c969343f168a0dfe9","target":"record","created_at":"2026-05-18T01:30:42Z","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":"a8cc46f484092222696caba607ccf22d2e8d5954071aa945a903f1518d811b33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-06T17:19:24Z","title_canon_sha256":"d5982acbd0d1f141ad59d6d3c6e923f715e68d2469f24f16d07a8291b1a788af"},"schema_version":"1.0","source":{"id":"1505.01437","kind":"arxiv","version":2}},"canonical_sha256":"fae14d9ba18195891b4dc7765b7f6b40fcc3add815a2253f7581bb73e595e3c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fae14d9ba18195891b4dc7765b7f6b40fcc3add815a2253f7581bb73e595e3c9","first_computed_at":"2026-05-18T01:30:42.883743Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:42.883743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3lKZ5V7HUfphVGFXXPJpRQrTRSPHYQdAysWyquCYrrmyJZZ8mI9QPpRs+xHjc5Eq7rHSwPtt9KNQ7ayNOCJdBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:42.884446Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.01437","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fbe1e1fbff34279a2205da4a8bc3e02949cc08ef9176e71c969343f168a0dfe9","sha256:184a28e9db6e8c67a97a402aa7183f4a7263e28596d73f7e68b8c2b6b09b7dca"],"state_sha256":"882aadad0b4fae5a2db349e032bbec26f061633c9898e8301ccde099a5d0891e"}