{"paper":{"title":"Path Portfolio Optimization: Defect, Lift, and the Price of Path Complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-fin.PM","authors_text":"Miquel Noguer i Alonso","submitted_at":"2026-08-03T15:06:00Z","abstract_excerpt":"This paper builds Path Portfolio Optimization: portfolio theory on a path-first framework in which the signature is the universal coordinate of the price path, and asks whether it survives estimation. A portfolio is a linear functional of the signature, so the control lives in a truncated tensor algebra, the covariance of signature coordinates is the non-group-like part of the expected signature --- a defect form --- and the whole mean--variance problem becomes a linear system in one tensor. Two structural results follow. The lift is the execution convention: the gap between the Marcus and for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.02355","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.02355/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}