{"paper":{"title":"Two versions of the fundamental theorem of asset pricing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Luca Pratelli, Patrizia Berti, Pietro Rigo","submitted_at":"2014-02-14T20:18:37Z","abstract_excerpt":"Let $L$ be a convex cone of real random variables on the probability space $(\\Omega,\\mathcal{A},P_0)$. The existence of a probability $P$ on $\\mathcal{A}$ such that $$ P \\sim P_0,\\quad E_P \\abs{X}< \\infty\\, \\text{ and } \\, E_P(X) \\leq 0\\, \\text{ for all }X \\in L $$ is investigated. Two results are provided. In the first, $P$ is a finitely additive probability, while $P$ is $\\sigma$-additive in the second. If $L$ is a linear space then $-X\\in L$ whenever $X\\in L$, so that $E_P(X)\\leq 0$ turns into $E_P(X)=0$. Hence, the results apply to various significant frameworks, including equivalent marti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3570","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":""},"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"}