{"paper":{"title":"General properties of the Solutions to Moving Boundary Problems for Black-Sholes Equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP","q-fin.MF"],"primary_cat":"q-fin.PR","authors_text":"Hyong-Chol O, Tae-Song Choe","submitted_at":"2022-03-11T02:44:25Z","abstract_excerpt":"We study general properties such as the solution representation of a moving boundary value problem of the Black-Scholes equation, its min-max estimation, lower and upper gradient estimates, and strict monotonicity with respect to the spatial variables of the solution. These results are used in the study of a structural model of pricing puttable bond with credit risk. We first prove the solution representation of a special fixed boundary value problem of the Black-Scholes equation, the min-max estimate, the lower and upper gradient estimates, and the strict monotonicity with respect to the spat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.05726","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/2203.05726/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"}