{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QLT2E337VIL6D6DVDHKCXPNOYA","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"60d6995faf7d845a274a3f765cfb6b39c604e5dbb1451b735b14fa98bb7fa7d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2016-11-03T05:30:13Z","title_canon_sha256":"55eeaca4589efa2afb76d332c989e2bdafef135af22ce03d191690cad0a486ce"},"schema_version":"1.0","source":{"id":"1611.00885","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.00885","created_at":"2026-05-18T00:31:03Z"},{"alias_kind":"arxiv_version","alias_value":"1611.00885v2","created_at":"2026-05-18T00:31:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.00885","created_at":"2026-05-18T00:31:03Z"},{"alias_kind":"pith_short_12","alias_value":"QLT2E337VIL6","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QLT2E337VIL6D6DV","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QLT2E337","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:2b2f283294d4ab7bacf7243a4b42e324fdd341bf1afe9e97ab4064ebb3c28b4f","target":"graph","created_at":"2026-05-18T00:31:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We investigate qualitative and quantitative behavior of a solution of the mathematical model for pricing American style of perpetual put options. We assume the option price is a solution to the stationary generalized Black-Scholes equation in which the volatility function may depend on the second derivative of the option price itself. We prove existence and uniqueness of a solution to the free boundary problem. We derive a single implicit equation for the free boundary position and the closed form formula for the option price. It is a generalization of the well-known explicit closed form solut","authors_text":"Daniel Sevcovic, Maria do Rosario Grossinho, Yaser Kord Faghan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2016-11-03T05:30:13Z","title":"Pricing Perpetual Put Options by the Black-Scholes Equation with a Nonlinear Volatility Function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00885","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5eab54ee2b42ea011eb0e085af8316518ba9458bcf15b513f5475a7d2c17ea40","target":"record","created_at":"2026-05-18T00:31:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"60d6995faf7d845a274a3f765cfb6b39c604e5dbb1451b735b14fa98bb7fa7d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.MF","submitted_at":"2016-11-03T05:30:13Z","title_canon_sha256":"55eeaca4589efa2afb76d332c989e2bdafef135af22ce03d191690cad0a486ce"},"schema_version":"1.0","source":{"id":"1611.00885","kind":"arxiv","version":2}},"canonical_sha256":"82e7a26f7faa17e1f87519d42bbdaec0271769c41aa18a3212287058cedec695","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"82e7a26f7faa17e1f87519d42bbdaec0271769c41aa18a3212287058cedec695","first_computed_at":"2026-05-18T00:31:03.156550Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:03.156550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lgj32zDV7svmhPe41UU9BNCPTb/ht3wq9SCr5+XaD2MRkHqcAMP4GOd44WYxBT9fuUd9vUaLSNZAIHRapcYqBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:03.157237Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.00885","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5eab54ee2b42ea011eb0e085af8316518ba9458bcf15b513f5475a7d2c17ea40","sha256:2b2f283294d4ab7bacf7243a4b42e324fdd341bf1afe9e97ab4064ebb3c28b4f"],"state_sha256":"8497098d82b6803089db6e3d61917e8a1327737c41612914fb5786798e00b9ae"}