{"id":"https://openalex.org/W2611074859","doi":"https://doi.org/10.1137/17m1130836","title":"Variational Analysis for Options with Stochastic Volatility and Multiple Factors","display_name":"Variational Analysis for Options with Stochastic Volatility and Multiple Factors","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2611074859","doi":"https://doi.org/10.1137/17m1130836","mag":"2611074859"},"language":"en","primary_location":{"id":"doi:10.1137/17m1130836","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1130836","pdf_url":null,"source":{"id":"https://openalex.org/S75627377","display_name":"SIAM Journal on Financial Mathematics","issn_l":"1945-497X","issn":["1945-497X"],"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 Financial Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.inria.fr/hal-01516011","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076843972","display_name":"J. Fr\u00e9d\u00e9ric Bonnans","orcid":"https://orcid.org/0000-0003-0988-9865"},"institutions":[{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I4210107641","display_name":"Centre de Math\u00e9matiques Appliqu\u00e9es","ror":"https://ror.org/012e1xn46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I142476485","https://openalex.org/I4210107641","https://openalex.org/I4210141950","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"J. Fr\u00e9d\u00e9ric Bonnans","raw_affiliation_strings":["Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems (Centre de Math\u00e9matiques Appliqu\u00e9es Ecole Polytechnique Route de Saclay 91128 Palaiseau - France)"],"affiliations":[{"raw_affiliation_string":"Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems (Centre de Math\u00e9matiques Appliqu\u00e9es Ecole Polytechnique Route de Saclay 91128 Palaiseau - France)","institution_ids":["https://openalex.org/I4210107641","https://openalex.org/I142476485"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071446522","display_name":"Axel Kr\u00f6ner","orcid":null},"institutions":[{"id":"https://openalex.org/I39343248","display_name":"Humboldt-Universit\u00e4t zu Berlin","ror":"https://ror.org/01hcx6992","country_code":"DE","type":"education","lineage":["https://openalex.org/I39343248"]},{"id":"https://openalex.org/I4210107641","display_name":"Centre de Math\u00e9matiques Appliqu\u00e9es","ror":"https://ror.org/012e1xn46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I142476485","https://openalex.org/I4210107641","https://openalex.org/I4210141950","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]}],"countries":["DE","FR"],"is_corresponding":false,"raw_author_name":"Axel Kr\u00f6ner","raw_affiliation_strings":["Institut f\u00fcr Mathematik [Humboldt] (Unter den Linden 6\r\n10099 Berlin\r\nGermany - Germany)","Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems (Centre de Math\u00e9matiques Appliqu\u00e9es Ecole Polytechnique Route de Saclay 91128 Palaiseau - France)"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik [Humboldt] (Unter den Linden 6\r\n10099 Berlin\r\nGermany - Germany)","institution_ids":["https://openalex.org/I39343248"]},{"raw_affiliation_string":"Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems (Centre de Math\u00e9matiques Appliqu\u00e9es Ecole Polytechnique Route de Saclay 91128 Palaiseau - France)","institution_ids":["https://openalex.org/I4210107641","https://openalex.org/I142476485"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5076843972"],"corresponding_institution_ids":["https://openalex.org/I142476485","https://openalex.org/I4210107641"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.00858645,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"9","issue":"2","first_page":"465","last_page":"492"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9998000264167786,"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":0.9998000264167786,"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/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9559999704360962,"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/T12011","display_name":"Insurance, Mortality, Demography, Risk Management","score":0.9455999732017517,"subfield":{"id":"https://openalex.org/subfields/3317","display_name":"Demography"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/stochastic-volatility","display_name":"Stochastic volatility","score":0.7212792634963989},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6568140983581543},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6185104250907898},{"id":"https://openalex.org/keywords/heston-model","display_name":"Heston model","score":0.6052826046943665},{"id":"https://openalex.org/keywords/sabr-volatility-model","display_name":"SABR volatility model","score":0.5709937214851379},{"id":"https://openalex.org/keywords/implied-volatility","display_name":"Implied volatility","score":0.5331810116767883},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.524983823299408},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.5096533298492432},{"id":"https://openalex.org/keywords/volatility","display_name":"Volatility (finance)","score":0.5090469717979431},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4974084198474884},{"id":"https://openalex.org/keywords/commutator","display_name":"Commutator","score":0.4668928384780884},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.44796329736709595},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3501613736152649},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2969790995121002},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20259320735931396},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.10571661591529846}],"concepts":[{"id":"https://openalex.org/C85393063","wikidata":"https://www.wikidata.org/wiki/Q596307","display_name":"Stochastic volatility","level":3,"score":0.7212792634963989},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6568140983581543},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6185104250907898},{"id":"https://openalex.org/C93045229","wikidata":"https://www.wikidata.org/wiki/Q5746554","display_name":"Heston model","level":5,"score":0.6052826046943665},{"id":"https://openalex.org/C187625094","wikidata":"https://www.wikidata.org/wiki/Q7388452","display_name":"SABR volatility model","level":4,"score":0.5709937214851379},{"id":"https://openalex.org/C24189920","wikidata":"https://www.wikidata.org/wiki/Q1660345","display_name":"Implied volatility","level":3,"score":0.5331810116767883},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.524983823299408},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.5096533298492432},{"id":"https://openalex.org/C91602232","wikidata":"https://www.wikidata.org/wiki/Q756115","display_name":"Volatility (finance)","level":2,"score":0.5090469717979431},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4974084198474884},{"id":"https://openalex.org/C145620117","wikidata":"https://www.wikidata.org/wiki/Q2989763","display_name":"Commutator","level":4,"score":0.4668928384780884},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.44796329736709595},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3501613736152649},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2969790995121002},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20259320735931396},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.10571661591529846},{"id":"https://openalex.org/C73648015","wikidata":"https://www.wikidata.org/wiki/Q6543817","display_name":"Lie conformal algebra","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/17m1130836","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1130836","pdf_url":null,"source":{"id":"https://openalex.org/S75627377","display_name":"SIAM Journal on Financial Mathematics","issn_l":"1945-497X","issn":["1945-497X"],"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 Financial Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01516011v1","is_oa":true,"landing_page_url":"https://hal.inria.fr/hal-01516011","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://hal.inria.fr/hal-01516011","raw_type":"\\ninfo:eu-repo/semantics/preprint\\n"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01516011v1","is_oa":true,"landing_page_url":"https://hal.inria.fr/hal-01516011","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://hal.inria.fr/hal-01516011","raw_type":"\\ninfo:eu-repo/semantics/preprint\\n"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320324478","display_name":"Fondation Math\u00e9matique Jacques Hadamard","ror":"https://ror.org/0153me927"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W130211666","https://openalex.org/W1525786255","https://openalex.org/W1597209545","https://openalex.org/W1604311391","https://openalex.org/W1645300797","https://openalex.org/W2011569301","https://openalex.org/W2046955945","https://openalex.org/W2061956999","https://openalex.org/W2064978316","https://openalex.org/W2728760061","https://openalex.org/W3021444882","https://openalex.org/W3122434727"],"related_works":["https://openalex.org/W3123155432","https://openalex.org/W1601881750","https://openalex.org/W2004330626","https://openalex.org/W2994814085","https://openalex.org/W1805757422","https://openalex.org/W297795963","https://openalex.org/W3204658926","https://openalex.org/W1491092204","https://openalex.org/W2064243848","https://openalex.org/W2024023936"],"abstract_inverted_index":{"This":[0,53],"paper":[1],"performs":[2],"a":[3,7,55],"variational":[4],"analysis":[5,60],"for":[6],"class":[8],"of":[9,20,23,35,42,57],"European":[10],"or":[11],"American":[12],"options":[13],"with":[14],"stochastic":[15],"volatility":[16],"models,":[17],"including":[18],"those":[19],"Heston":[21],"and":[22,25,32,64],"Achdou":[24,63],"Tchou.":[26],"Taking":[27],"into":[28],"account":[29],"partial":[30,45],"correlations":[31],"the":[33,40,43,58],"presence":[34],"multiple":[36],"factors,":[37],"we":[38],"obtain":[39],"well-posedness":[41],"related":[44],"differential":[46],"equations,":[47],"in":[48,66],"some":[49],"weighted":[50],"Sobolev":[51],"spaces.":[52],"involves":[54],"generalization":[56],"commutator":[59],"introduced":[61],"by":[62],"Tchou":[65],"[ESAIM":[67],"Math.":[68],"Model.":[69],"Numer.":[70],"Anal.,":[71],"36":[72],"(2002),":[73],"pp.":[74],"373--395].":[75]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}