{"id":"https://openalex.org/W7214949400","doi":"https://doi.org/10.48550/arxiv.2609.36447","title":"Derivation of the General Solution of the Black-Scholes Boundary-Value Problem","display_name":"Derivation of the General Solution of the Black-Scholes Boundary-Value Problem","publication_year":2026,"publication_date":"2026-09-29","ids":{"openalex":"https://openalex.org/W7214949400","doi":"https://doi.org/10.48550/arxiv.2609.36447"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.36447","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36447","pdf_url":"https://arxiv.org/pdf/2609.36447","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.36447","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110079883","display_name":"ByoungSeon Choi","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Choi, ByoungSeon","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5153593810","display_name":"M. Y. Choi","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Choi, M. Y.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/black-scholes-equation","display_name":"Black-Scholes equation","score":0.9179999828338623},{"id":"https://openalex.org/keywords/boundary-value-problems","display_name":"boundary value problems","score":0.8289999961853027},{"id":"https://openalex.org/keywords/european-call-options","display_name":"European call options","score":0.8849999904632568},{"id":"https://openalex.org/keywords/general-solution","display_name":"general solution","score":0.5440000295639038},{"id":"https://openalex.org/keywords/uniqueness-of-solutions","display_name":"uniqueness of solutions","score":0.6819999814033508},{"id":"https://openalex.org/keywords/law-of-one-price","display_name":"law of one price","score":0.9750000238418579},{"id":"https://openalex.org/keywords/option-pricing","display_name":"option pricing","score":0.7559999823570251},{"id":"https://openalex.org/keywords/terminal-conditions","display_name":"terminal conditions","score":0.6039999723434448}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6255000233650208},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5284000039100647},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43230000138282776},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3750999867916107},{"id":"https://openalex.org/C2779664074","wikidata":"https://www.wikidata.org/wiki/Q3518405","display_name":"Terminal (telecommunication)","level":2,"score":0.3677999973297119},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.36719998717308044},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.3476000130176544},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.3450999855995178},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3409000039100647},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3352999985218048},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.33480000495910645},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.32739999890327454},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.31790000200271606},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.30640000104904175},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.2935999929904938},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.29249998927116394},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.28130000829696655},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.25529998540878296},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.25200000405311584}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.36447","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36447","pdf_url":"https://arxiv.org/pdf/2609.36447","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.36447","doi":"https://doi.org/10.48550/arxiv.2609.36447","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.36447","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.36447","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36447","pdf_url":"https://arxiv.org/pdf/2609.36447","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214949400.pdf","grobid_xml":"https://content.openalex.org/works/W7214949400.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W2077791698","https://openalex.org/W2808856268","https://openalex.org/W3150592043"],"related_works":["https://openalex.org/W2808856268","https://openalex.org/W6981012713","https://openalex.org/W130715350","https://openalex.org/W2253841636","https://openalex.org/W4254611757","https://openalex.org/W3203070967","https://openalex.org/W2092495738","https://openalex.org/W2488161314","https://openalex.org/W4410891381","https://openalex.org/W2352898628"],"abstract_inverted_index":{"There":[0],"are":[1],"infinitely":[2],"many":[3],"functions":[4],"that":[5,24],"satisfy":[6],"the":[7,13,18,25,31,34,43,53,60,79],"Black-Scholes":[8,26,80],"partial":[9],"differential":[10],"equation":[11],"and":[12,65],"terminal":[14],"condition":[15],"corresponding":[16],"to":[17,30,78],"European":[19],"call":[20],"option.":[21],"This":[22],"means":[23],"formula,":[27],"which":[28],"led":[29],"award":[32],"of":[33,55,59,63,75],"1997":[35],"Nobel":[36],"Prize":[37],"in":[38],"Economic":[39],"Sciences,":[40],"is":[41],"not":[42],"unique":[44],"solution,":[45],"as":[46],"was":[47],"once":[48],"assumed.":[49],"Consequently,":[50],"it":[51],"violates":[52],"law":[54],"one":[56,58],"price,":[57],"fundamental":[61],"laws":[62],"economics":[64],"finance.":[66],"In":[67],"this":[68],"article,":[69],"we":[70],"present":[71],"a":[72],"rigorous":[73],"derivation":[74],"these":[76],"solutions":[77],"boundary":[81],"value":[82],"problem.":[83]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-01T00:00:00"}