{"paper":{"title":"Note on the Weak Convergence of Hyperplane $\\alpha$-Quantile Functionals and Their Continuity in the Skorokhod J1 Topology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Pietro Maria Sparago","submitted_at":"2026-05-19T20:36:39Z","abstract_excerpt":"The ${\\alpha}$-quantile of a stochastic process $M_{t,{\\alpha}}$ has been introduced in Miura (Hitotsubashi J Commerce Manag 27(1):15-28, 1992), and important distributional results have been derived in Akahori (Ann Appl Probab 5(2):383-388, 1995), Dassios (Ann Appl Probab 5(2):389-398, 1995) and Yor (J Appl Probab 32(2):405-416, 1995), with special attention given to the problem of pricing ${\\alpha}$-quantile options. We straightforwardly extend the classical monodimensional setting to $\\mathbb{R}^d$ by introducing the hyperplane ${\\alpha}$-quantile, and we find an explicit functional continu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20471","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/2605.20471/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"}