{"id":"https://openalex.org/W2949725202","doi":"https://doi.org/10.1137/070686494","title":"A Proof of the Smoothness of the Finite Time Horizon American Put Option for Jump Diffusions","display_name":"A Proof of the Smoothness of the Finite Time Horizon American Put Option for Jump Diffusions","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2949725202","doi":"https://doi.org/10.1137/070686494","mag":"2949725202"},"language":"en","primary_location":{"id":"doi:10.1137/070686494","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070686494","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/math/0703782","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005237318","display_name":"Erhan Bayraktar","orcid":"https://orcid.org/0000-0002-1926-4570"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Erhan Bayraktar","raw_affiliation_strings":["[email\u00a0protected]#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[email\u00a0protected]#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5005237318"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.41578629,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"48","issue":"2","first_page":"551","last_page":"572"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9994000196456909,"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":0.9994000196456909,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9912999868392944,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9430000185966492,"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/mathematics","display_name":"Mathematics","score":0.7754555344581604},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6249531507492065},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.5806342363357544},{"id":"https://openalex.org/keywords/optimal-stopping","display_name":"Optimal stopping","score":0.5448006987571716},{"id":"https://openalex.org/keywords/jump-diffusion","display_name":"Jump diffusion","score":0.541694164276123},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.5410910844802856},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5179623365402222},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5061795115470886},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.47813141345977783},{"id":"https://openalex.org/keywords/limit-of-a-sequence","display_name":"Limit of a sequence","score":0.4683011770248413},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4518529772758484},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4399183988571167},{"id":"https://openalex.org/keywords/free-boundary-problem","display_name":"Free boundary problem","score":0.43771928548812866},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.42868998646736145},{"id":"https://openalex.org/keywords/jump","display_name":"Jump","score":0.37617993354797363},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3694717288017273},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.33577972650527954},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.18920856714248657},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.1438038945198059}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7754555344581604},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6249531507492065},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.5806342363357544},{"id":"https://openalex.org/C99414536","wikidata":"https://www.wikidata.org/wiki/Q7098950","display_name":"Optimal stopping","level":2,"score":0.5448006987571716},{"id":"https://openalex.org/C2779664328","wikidata":"https://www.wikidata.org/wiki/Q6311158","display_name":"Jump diffusion","level":3,"score":0.541694164276123},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.5410910844802856},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5179623365402222},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5061795115470886},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.47813141345977783},{"id":"https://openalex.org/C71287196","wikidata":"https://www.wikidata.org/wiki/Q847204","display_name":"Limit of a sequence","level":3,"score":0.4683011770248413},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4518529772758484},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4399183988571167},{"id":"https://openalex.org/C154416045","wikidata":"https://www.wikidata.org/wiki/Q5500196","display_name":"Free boundary problem","level":3,"score":0.43771928548812866},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.42868998646736145},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.37617993354797363},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3694717288017273},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.33577972650527954},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.18920856714248657},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.1438038945198059},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":13,"locations":[{"id":"doi:10.1137/070686494","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070686494","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:math/0703782","is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0703782","pdf_url":"https://arxiv.org/pdf/math/0703782","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,"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":"mag:2949725202","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/math/0703782","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,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.239.3948","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.239.3948","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0703782v10.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.239.4499","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.239.4499","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0703782v7.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.239.550","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.239.550","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0703782v6.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.239.6789","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.239.6789","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0703782v4.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.239.8505","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.239.8505","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0703782v2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.239.8807","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.239.8807","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0703782v5.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.240.1522","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.240.1522","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0703782v12.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.240.348","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.240.348","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0703782v9.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.241.5247","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.241.5247","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0703782v11.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.math/0703782","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.math/0703782","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,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:math/0703782","is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0703782","pdf_url":"https://arxiv.org/pdf/math/0703782","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,"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":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2949725202.pdf","grobid_xml":"https://content.openalex.org/works/W2949725202.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W604762380","https://openalex.org/W1494628843","https://openalex.org/W2015228311","https://openalex.org/W2027196449","https://openalex.org/W2056360380","https://openalex.org/W2073187583","https://openalex.org/W2115527256","https://openalex.org/W2124403419","https://openalex.org/W2126311658","https://openalex.org/W2149747548","https://openalex.org/W3002174615","https://openalex.org/W3124480685","https://openalex.org/W4231495859","https://openalex.org/W4247206600"],"related_works":["https://openalex.org/W3122121291","https://openalex.org/W2291121065","https://openalex.org/W2951493944","https://openalex.org/W1017851796","https://openalex.org/W2752018821","https://openalex.org/W1548287612","https://openalex.org/W2206139918","https://openalex.org/W3126654557","https://openalex.org/W2109753894","https://openalex.org/W3093238748","https://openalex.org/W2289548509","https://openalex.org/W2282414242","https://openalex.org/W2141154142","https://openalex.org/W2785902690","https://openalex.org/W2615866445","https://openalex.org/W2465125241","https://openalex.org/W2949198466","https://openalex.org/W2043204925","https://openalex.org/W3122991843","https://openalex.org/W1966195514"],"abstract_inverted_index":{"We":[0,42],"give":[1],"a":[2,21,29,38,124,133,142,170,175,208],"new":[3,119],"proof":[4,100,120],"of":[5,12,37,64,69,75,105,127,130,136,151,178,184],"the":[6,9,13,25,34,46,52,61,99,103,148,152,157,190,194,199],"fact":[7],"that":[8,45,101,173],"value":[10,47,134,149,200],"function":[11,48,135,150,201],"finite":[14],"time":[15],"horizon":[16],"American":[17,153],"put":[18,154],"option":[19,155],"for":[20,141,156],"jump":[22,158],"diffusion,":[23],"when":[24],"jumps":[26],"are":[27],"from":[28],"compound":[30],"Poisson":[31],"process,":[32],"is":[33,49,95,132,166],"classical":[35,62,182],"solution":[36],"free":[39,186],"boundary":[40,187],"equation.":[41],"also":[43],"show":[44],"$C^1$":[50],"across":[51],"optimal":[53,138],"stopping":[54,139],"boundary.":[55],"Our":[56],"proof,":[57],"which":[58,131],"uses":[59,102],"only":[60],"theory":[63,104],"parabolic":[65],"partial":[66],"differential":[67],"equations":[68],"[A.":[70,84],"Friedman,":[71,85],"Partial":[72],"Differential":[73,87],"Equations":[74,88],"Parabolic":[76],"Type,":[77],"Prentice\u2013Hall,":[78],"Englewood":[79],"Cliffs,":[80],"NJ,":[81],"1964]":[82],"and":[83,89,161],"Stochastic":[86],"Applications,":[90],"Dover,":[91],"Mineola,":[92],"NY,":[93],"2006],":[94],"an":[96,137],"alternative":[97],"to":[98,147,181,198,207],"viscosity":[106],"solutions":[107,183],"(see":[108],"[H.":[109],"Pham,":[110],"Appl.":[111],"Math.":[112],"Optim.,":[113],"35":[114],"(1997),":[115],"pp.":[116],"145\u2013164]).":[117],"This":[118,164],"relies":[121],"on":[122],"constructing":[123],"monotonous":[125],"sequence":[126,165,196],"functions,":[128],"each":[129],"problem":[140],"geometric":[143],"Brownian":[144],"motion,":[145],"converging":[146],"diffusion":[159],"uniformly":[160],"exponentially":[162,202],"fast.":[163],"constructed":[167],"by":[168],"iterating":[169],"functional":[171],"operator":[172],"maps":[174],"certain":[176],"class":[177],"convex":[179],"functions":[180],"corresponding":[185],"equations.":[188],"On":[189],"other":[191],"hand,":[192],"since":[193],"approximating":[195],"converges":[197],"fast,":[203],"it":[204],"naturally":[205],"leads":[206],"good":[209],"numerical":[210],"scheme.":[211]},"counts_by_year":[],"updated_date":"2026-09-04T10:56:28.161419","created_date":"2025-10-10T00:00:00"}
