{"id":"https://openalex.org/W2124861454","doi":"https://doi.org/10.1137/06065324x","title":"Barrier Option Hedging under Constraints: A Viscosity Approach","display_name":"Barrier Option Hedging under Constraints: A Viscosity Approach","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2124861454","doi":"https://doi.org/10.1137/06065324x","mag":"2124861454"},"language":"en","primary_location":{"id":"doi:10.1137/06065324x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/06065324x","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":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063880124","display_name":"Imen Bentahar","orcid":null},"institutions":[{"id":"https://openalex.org/I4210131891","display_name":"l'Assurance Maladie","ror":"https://ror.org/03am7sg53","country_code":"FR","type":"other","lineage":["https://openalex.org/I4210131891"]},{"id":"https://openalex.org/I4210147464","display_name":"Laboratoire de Probabilit\u00e9s et Mod\u00e8les Al\u00e9atoires","ror":"https://ror.org/04hjc7403","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210147464"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Imen Bentahar","raw_affiliation_strings":["LPMA - Laboratoire de Probabilit\u00e9s et Mod\u00e8les Al\u00e9atoires (France)","LFA - Laboratoire de Finance Assurance (15, boulevard Gabriel P\u00e9ri 92245 Malakoff Cedex - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LPMA - Laboratoire de Probabilit\u00e9s et Mod\u00e8les Al\u00e9atoires (France)","institution_ids":["https://openalex.org/I4210147464"]},{"raw_affiliation_string":"LFA - Laboratoire de Finance Assurance (15, boulevard Gabriel P\u00e9ri 92245 Malakoff Cedex - France)","institution_ids":["https://openalex.org/I4210131891"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030868049","display_name":"Bruno Bouchard","orcid":"https://orcid.org/0000-0002-4716-1253"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Bruno Bouchard","raw_affiliation_strings":["Institut f\u00fcr Mathematik [Berlin] (Sekr. MA 4-1 Stra\u00dfe des 17.Juni 136 10623 Berlin - Germany)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik [Berlin] (Sekr. MA 4-1 Stra\u00dfe des 17.Juni 136 10623 Berlin - Germany)","institution_ids":["https://openalex.org/I4577782"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2265,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.84443544,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"45","issue":"5","first_page":"1846","last_page":"1874"},"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9778000116348267,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9578999876976013,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8028793334960938},{"id":"https://openalex.org/keywords/viscosity-solution","display_name":"Viscosity solution","score":0.631402313709259},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.6014305949211121},{"id":"https://openalex.org/keywords/hedge","display_name":"Hedge","score":0.5609076023101807},{"id":"https://openalex.org/keywords/barrier-option","display_name":"Barrier option","score":0.5475408434867859},{"id":"https://openalex.org/keywords/dirichlet-problem","display_name":"Dirichlet problem","score":0.4860308766365051},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.47905978560447693},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.46299394965171814},{"id":"https://openalex.org/keywords/asset","display_name":"Asset (computer security)","score":0.4533129036426544},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4416447877883911},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4396519660949707},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.42426568269729614},{"id":"https://openalex.org/keywords/brownian-motion","display_name":"Brownian motion","score":0.4137133061885834},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37143585085868835},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.30784308910369873},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25561195611953735},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09772986173629761},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08133566379547119}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8028793334960938},{"id":"https://openalex.org/C88731125","wikidata":"https://www.wikidata.org/wiki/Q7935676","display_name":"Viscosity solution","level":2,"score":0.631402313709259},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.6014305949211121},{"id":"https://openalex.org/C70771513","wikidata":"https://www.wikidata.org/wiki/Q235779","display_name":"Hedge","level":2,"score":0.5609076023101807},{"id":"https://openalex.org/C2776631005","wikidata":"https://www.wikidata.org/wiki/Q808919","display_name":"Barrier option","level":2,"score":0.5475408434867859},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.4860308766365051},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.47905978560447693},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.46299394965171814},{"id":"https://openalex.org/C76178495","wikidata":"https://www.wikidata.org/wiki/Q4808784","display_name":"Asset (computer security)","level":2,"score":0.4533129036426544},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4416447877883911},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4396519660949707},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.42426568269729614},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.4137133061885834},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37143585085868835},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.30784308910369873},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25561195611953735},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09772986173629761},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08133566379547119},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/06065324x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/06065324x","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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/8","score":0.44999998807907104,"display_name":"Decent work and economic growth"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1487555560","https://openalex.org/W1866311589","https://openalex.org/W1983652428","https://openalex.org/W2021318678","https://openalex.org/W2025951566","https://openalex.org/W2032316144","https://openalex.org/W2042775870","https://openalex.org/W2051220807","https://openalex.org/W2075749097","https://openalex.org/W2086565819","https://openalex.org/W2105911220","https://openalex.org/W2128350654","https://openalex.org/W2141177818","https://openalex.org/W2177195156","https://openalex.org/W2493936716","https://openalex.org/W3124371155","https://openalex.org/W3125183157"],"related_works":["https://openalex.org/W1766831359","https://openalex.org/W2098823792","https://openalex.org/W2001501870","https://openalex.org/W2130123026","https://openalex.org/W2158765561","https://openalex.org/W2146761690","https://openalex.org/W4303700441","https://openalex.org/W3123099579","https://openalex.org/W4298014529","https://openalex.org/W4300200796"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,6,21,42,55,60,101,127],"problem":[3],"of":[4,23,25,44,54,62,116],"finding":[5],"minimal":[7],"initial":[8],"capital":[9],"needed":[10],"in":[11,28,36],"order":[12],"to":[13,34],"hedge":[14],"without":[15],"risk":[16],"a":[17,37,45,51,95,106,110,114,124],"barrier":[18],"option":[19],"when":[20],"vector":[22],"proportions":[24],"wealth":[26],"invested":[27],"each":[29],"risky":[30],"asset":[31],"is":[32],"constrained":[33],"lie":[35],"closed":[38],"convex":[39],"domain.":[40],"In":[41],"context":[43],"Brownian":[46],"diffusion":[47],"model,":[48],"we":[49,108],"provide":[50],"PDE":[52],"characterization":[53],"superhedging":[56,103],"price.":[57,104],"This":[58],"extends":[59],"result":[61],"Broadie,":[63],"Cvitani,":[64,75],"and":[65,74,77,93],"Soner":[66],"[Rev.":[67],"Financial":[68],"Stud.,":[69],"11":[70],"(1998),":[71],"pp.":[72,84],"59\u201379]":[73],"Pham,":[76],"Touzi":[78],"[J.":[79],"Appl.":[80],"Probab.,":[81],"36":[82],"(1999),":[83],"523\u2013545]":[85],"which":[86],"was":[87],"obtained":[88],"for":[89,99,113],"plain":[90],"vanilla":[91],"options":[92],"provides":[94],"natural":[96],"numerical":[97],"procedure":[98],"computing":[100],"corresponding":[102],"As":[105],"by\u2010product,":[107],"obtain":[109],"comparison":[111],"theorem":[112],"class":[115],"parabolic":[117],"PDEs":[118],"with":[119],"relaxed":[120],"Dirichlet":[121],"conditions":[122],"involving":[123],"constraint":[125],"on":[126],"gradient.":[128]},"counts_by_year":[{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2016-06-24T00:00:00"}
