{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JBRXXKO56UMPH4KJOL42Z3R5OC","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":"43d2f0e353339fed483b343b507d822d8df80de65b8a204d1d5a61989356a517","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-13T09:05:24Z","title_canon_sha256":"a1ee6211e1b9a90f15a61dd82f62fac54f07658bb5ac018c3221803b20b60874"},"schema_version":"1.0","source":{"id":"1208.2527","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.2527","created_at":"2026-05-18T03:48:57Z"},{"alias_kind":"arxiv_version","alias_value":"1208.2527v1","created_at":"2026-05-18T03:48:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2527","created_at":"2026-05-18T03:48:57Z"},{"alias_kind":"pith_short_12","alias_value":"JBRXXKO56UMP","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JBRXXKO56UMPH4KJ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JBRXXKO5","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:bbffe888c219d642d62a6161d716adc497325459634a8fd876b85f73bbee8c06","target":"graph","created_at":"2026-05-18T03:48:57Z","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":"In finance, the price of a volatile asset can be modeled using fractional Brownian motion (fBm) with Hurst parameter $H>1/2.$ The Black-Scholes model for the values of returns of an asset using fBm is given as, [Y_t=Y_0 \\exp{((r+\\mu)t+\\sigma B_t^H)}, t\\geq 0], where $Y_0$ is the initial value, $r$ is constant interest rate, $\\mu$ is constant drift and $\\sigma$ is constant diffusion coefficient of fBm, which is denoted by $(B_t^H)$ where $t \\geq 0.$ Black-Scholes model can be constructed with some Markov processes such as Brownian motion. The advantage of modeling with fBm to Markov proccesses ","authors_text":"Ceren Vardar, Mine Caglar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-13T09:05:24Z","title":"Distribution of Maximum Loss for Fractional Brownian Motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2527","kind":"arxiv","version":1},"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":"sha256:2ec9cc69f8edee7f41ef2b0018288772d1a8c46b9392486bc6348b511cc5d872","target":"record","created_at":"2026-05-18T03:48:57Z","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":"43d2f0e353339fed483b343b507d822d8df80de65b8a204d1d5a61989356a517","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-13T09:05:24Z","title_canon_sha256":"a1ee6211e1b9a90f15a61dd82f62fac54f07658bb5ac018c3221803b20b60874"},"schema_version":"1.0","source":{"id":"1208.2527","kind":"arxiv","version":1}},"canonical_sha256":"48637ba9ddf518f3f14972f9acee3d709af90ab9ca0aae8d2ac23f2b574f5a25","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48637ba9ddf518f3f14972f9acee3d709af90ab9ca0aae8d2ac23f2b574f5a25","first_computed_at":"2026-05-18T03:48:57.628413Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:57.628413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x8U88BguDCMBlOqQxzZ0ce7/jjk4G2A/3J+AiW0TNS/yfnecw0RLrp9mTCL7AwpCKzTzsL78s+ixWbqetp3BAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:57.628891Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.2527","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ec9cc69f8edee7f41ef2b0018288772d1a8c46b9392486bc6348b511cc5d872","sha256:bbffe888c219d642d62a6161d716adc497325459634a8fd876b85f73bbee8c06"],"state_sha256":"d2bf5e5f220c8cd3c4134669af2bc86b1e7c9eb76075bb6f8d4c108ba0310ba9"}