{"paper":{"title":"Finitely additive equivalent martingale measures","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":"2010-12-13T17:40:06Z","abstract_excerpt":"Let $L$ be a linear space of real bounded random variables on the probability space $(\\Omega,\\mathcal{A},P_0)$. There is a finitely additive probability $P$ on $\\mathcal{A}$, such that $P\\sim P_0$ and $E_P(X)=0$ for all $X\\in L$, if and only if $c\\,E_Q(X)\\leq\\text{ess sup}(-X)$, $X\\in L$, for some constant $c>0$ and (countably additive) probability $Q$ on $\\mathcal{A}$ such that $Q\\sim P_0$. A necessary condition for such a $P$ to exist is $\\bar{L-L_\\infty^+}\\,\\cap L_\\infty^+=\\{0\\}$, where the closure is in the norm-topology. If $P_0$ is atomic, the condition is sufficient as well. In addition"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2811","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"}