{"paper":{"title":"On the Structural Foundations of Signature Volatility Models: Existence, Arbitrage, Completeness, and the Hedging-Error Decomposition","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"q-fin.MF","authors_text":"Akmal Xodarev","submitted_at":"2026-05-16T20:26:25Z","abstract_excerpt":"We establish four structural results for signature volatility models. First, we prove global existence and uniqueness of strong solutions to the signature SDE $dS_t = S_t \\langle \\ell, \\widehat{W}_t \\rangle \\, dB_t$ on the weighted tensor algebra $T_w$, identifying the admissibility class through a summability condition H1 and an exponential-integrability condition H3 for the square-integrable stochastic-exponential construction. Second, we establish the asset-pricing part on the natural filtration of the prolonged signature and separate it from transform non-explosion: H3 makes the reference-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.17142","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/2605.17142/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T22:33:23.771063Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T22:01:58.007733Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"fd7cfb9f02898b503e24523be472dc2e05fe5f269ac30181d08703e4df661fc4"},"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"}