{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:JBRXXKO56UMPH4KJOL42Z3R5OC","short_pith_number":"pith:JBRXXKO5","schema_version":"1.0","canonical_sha256":"48637ba9ddf518f3f14972f9acee3d709af90ab9ca0aae8d2ac23f2b574f5a25","source":{"kind":"arxiv","id":"1208.2527","version":1},"attestation_state":"computed","paper":{"title":"Distribution of Maximum Loss for Fractional Brownian Motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ceren Vardar, Mine Caglar","submitted_at":"2012-08-13T09:05:24Z","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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1208.2527","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-13T09:05:24Z","cross_cats_sorted":[],"title_canon_sha256":"a1ee6211e1b9a90f15a61dd82f62fac54f07658bb5ac018c3221803b20b60874","abstract_canon_sha256":"43d2f0e353339fed483b343b507d822d8df80de65b8a204d1d5a61989356a517"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:57.628891Z","signature_b64":"x8U88BguDCMBlOqQxzZ0ce7/jjk4G2A/3J+AiW0TNS/yfnecw0RLrp9mTCL7AwpCKzTzsL78s+ixWbqetp3BAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48637ba9ddf518f3f14972f9acee3d709af90ab9ca0aae8d2ac23f2b574f5a25","last_reissued_at":"2026-05-18T03:48:57.628413Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:57.628413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Distribution of Maximum Loss for Fractional Brownian Motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ceren Vardar, Mine Caglar","submitted_at":"2012-08-13T09:05:24Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2527","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1208.2527","created_at":"2026-05-18T03:48:57.628478+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.2527v1","created_at":"2026-05-18T03:48:57.628478+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2527","created_at":"2026-05-18T03:48:57.628478+00:00"},{"alias_kind":"pith_short_12","alias_value":"JBRXXKO56UMP","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_16","alias_value":"JBRXXKO56UMPH4KJ","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_8","alias_value":"JBRXXKO5","created_at":"2026-05-18T12:27:11.947152+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JBRXXKO56UMPH4KJOL42Z3R5OC","json":"https://pith.science/pith/JBRXXKO56UMPH4KJOL42Z3R5OC.json","graph_json":"https://pith.science/api/pith-number/JBRXXKO56UMPH4KJOL42Z3R5OC/graph.json","events_json":"https://pith.science/api/pith-number/JBRXXKO56UMPH4KJOL42Z3R5OC/events.json","paper":"https://pith.science/paper/JBRXXKO5"},"agent_actions":{"view_html":"https://pith.science/pith/JBRXXKO56UMPH4KJOL42Z3R5OC","download_json":"https://pith.science/pith/JBRXXKO56UMPH4KJOL42Z3R5OC.json","view_paper":"https://pith.science/paper/JBRXXKO5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.2527&json=true","fetch_graph":"https://pith.science/api/pith-number/JBRXXKO56UMPH4KJOL42Z3R5OC/graph.json","fetch_events":"https://pith.science/api/pith-number/JBRXXKO56UMPH4KJOL42Z3R5OC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JBRXXKO56UMPH4KJOL42Z3R5OC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JBRXXKO56UMPH4KJOL42Z3R5OC/action/storage_attestation","attest_author":"https://pith.science/pith/JBRXXKO56UMPH4KJOL42Z3R5OC/action/author_attestation","sign_citation":"https://pith.science/pith/JBRXXKO56UMPH4KJOL42Z3R5OC/action/citation_signature","submit_replication":"https://pith.science/pith/JBRXXKO56UMPH4KJOL42Z3R5OC/action/replication_record"}},"created_at":"2026-05-18T03:48:57.628478+00:00","updated_at":"2026-05-18T03:48:57.628478+00:00"}