{"paper":{"title":"On random convex analysis -- the analytic foundation of the module approach to conditional risk measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.RM"],"primary_cat":"math.FA","authors_text":"Shien Zhao, Tiexin Guo, Xiaolin Zeng","submitted_at":"2012-10-05T12:33:35Z","abstract_excerpt":"To provide a solid analytic foundation for the module approach to conditional risk measures, this paper establishes a complete random convex analysis over random locally convex modules by simultaneously considering the two kinds of topologies (namely the $(\\varepsilon,\\lambda)$--topology and the locally $L^0$-- convex topology). Then, we make use of the advantage of the $(\\varepsilon,\\lambda)$--topology and grasp the local property of $L^0$--convex conditional risk measures to prove that every $L^{0}$--convex $L^{p}$--conditional risk measure ($1\\leq p\\leq+\\infty$) can be uniquely extended to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1848","kind":"arxiv","version":6},"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"}