{"id":"https://openalex.org/W3135196308","doi":"https://doi.org/10.1137/21m1402170","title":"Pricing High-Dimensional Bermudan Options with Hierarchical Tensor Formats","display_name":"Pricing High-Dimensional Bermudan Options with Hierarchical Tensor Formats","publication_year":2023,"publication_date":"2023-04-24","ids":{"openalex":"https://openalex.org/W3135196308","doi":"https://doi.org/10.1137/21m1402170","mag":"3135196308"},"language":"en","primary_location":{"id":"doi:10.1137/21m1402170","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1402170","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":"http://arxiv.org/pdf/2103.01934","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042780618","display_name":"Christian Bayer","orcid":"https://orcid.org/0000-0002-9116-0039"},"institutions":[{"id":"https://openalex.org/I4210092021","display_name":"Weierstrass Institute for Applied Analysis and Stochastics","ror":"https://ror.org/00h1x4t21","country_code":"DE","type":"facility","lineage":["https://openalex.org/I315704651","https://openalex.org/I4210092021"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Christian Bayer","raw_affiliation_strings":["Weierstrass Institute for Applied Analysis and Stochastics, Berlin, 10117, Germany"],"raw_orcid":"https://orcid.org/0000-0002-9116-0039","affiliations":[{"raw_affiliation_string":"Weierstrass Institute for Applied Analysis and Stochastics, Berlin, 10117, Germany","institution_ids":["https://openalex.org/I4210092021"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046617182","display_name":"Martin Eigel","orcid":"https://orcid.org/0000-0003-2687-4497"},"institutions":[{"id":"https://openalex.org/I4210092021","display_name":"Weierstrass Institute for Applied Analysis and Stochastics","ror":"https://ror.org/00h1x4t21","country_code":"DE","type":"facility","lineage":["https://openalex.org/I315704651","https://openalex.org/I4210092021"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin Eigel","raw_affiliation_strings":["Weierstrass Institute for Applied Analysis and Stochastics, Berlin, 10117, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Weierstrass Institute for Applied Analysis and Stochastics, Berlin, 10117, Germany","institution_ids":["https://openalex.org/I4210092021"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014942878","display_name":"Leon Sallandt","orcid":"https://orcid.org/0000-0002-7102-7767"},"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":"Leon Sallandt","raw_affiliation_strings":["Technische Universit\u00e4t Berlin, Institut f\u00fcr Mathematik, Berlin, 10623, Germany"],"raw_orcid":"https://orcid.org/0000-0002-7102-7767","affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Berlin, Institut f\u00fcr Mathematik, Berlin, 10623, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057535604","display_name":"Philipp Trunschke","orcid":"https://orcid.org/0000-0002-2995-126X"},"institutions":[{"id":"https://openalex.org/I4210153365","display_name":"Laboratoire de Math\u00e9matiques Jean Leray","ror":"https://ror.org/04g1hjn96","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210141950","https://openalex.org/I4210153365","https://openalex.org/I97188460"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Philipp Trunschke","raw_affiliation_strings":["Nantes Universit\u00e9, Laboratoire de Math\u00e9matiques Jean Leray, Nantes, 44321, France"],"raw_orcid":"https://orcid.org/0000-0002-2995-126X","affiliations":[{"raw_affiliation_string":"Nantes Universit\u00e9, Laboratoire de Math\u00e9matiques Jean Leray, Nantes, 44321, France","institution_ids":["https://openalex.org/I4210153365"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5042780618"],"corresponding_institution_ids":["https://openalex.org/I4210092021"],"apc_list":null,"apc_paid":null,"fwci":1.8537,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.85035629,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"14","issue":"2","first_page":"383","last_page":"406"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational 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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.988099992275238,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.6898333430290222},{"id":"https://openalex.org/keywords/monte-carlo-methods-for-option-pricing","display_name":"Monte Carlo methods for option pricing","score":0.682584285736084},{"id":"https://openalex.org/keywords/valuation-of-options","display_name":"Valuation of options","score":0.5246598720550537},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5130964517593384},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5097975134849548},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.5048878788948059},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5035423636436462},{"id":"https://openalex.org/keywords/martingale","display_name":"Martingale (probability theory)","score":0.4700649678707123},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.4526786506175995},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.41306576132774353},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3936087489128113},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3746602237224579},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3347727060317993},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.17859086394309998},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15805694460868835}],"concepts":[{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.6898333430290222},{"id":"https://openalex.org/C101710237","wikidata":"https://www.wikidata.org/wiki/Q6904701","display_name":"Monte Carlo methods for option pricing","level":3,"score":0.682584285736084},{"id":"https://openalex.org/C194483076","wikidata":"https://www.wikidata.org/wiki/Q380382","display_name":"Valuation of options","level":2,"score":0.5246598720550537},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5130964517593384},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5097975134849548},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5048878788948059},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5035423636436462},{"id":"https://openalex.org/C48406656","wikidata":"https://www.wikidata.org/wiki/Q534112","display_name":"Martingale (probability theory)","level":2,"score":0.4700649678707123},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.4526786506175995},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.41306576132774353},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3936087489128113},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3746602237224579},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3347727060317993},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.17859086394309998},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15805694460868835},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/21m1402170","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1402170","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:RePEc:arx:papers:2103.01934","is_oa":true,"landing_page_url":null,"pdf_url":"http://arxiv.org/pdf/2103.01934","source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"preprint"},{"id":"pmh:doi:10.20347/wias.preprint.2821","is_oa":false,"landing_page_url":"https://archive.wias-berlin.de/receive/wias_mods_00007487?XSL.Transformer=mods","pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"preprint"},{"id":"pmh:oai:HAL:hal-05317324v1","is_oa":false,"landing_page_url":"https://hal.science/hal-05317324","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Financial Mathematics, 2023, 14 (2), pp.383-406. ⟨10.1137/21M1402170⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:RePEc:arx:papers:2103.01934","is_oa":true,"landing_page_url":null,"pdf_url":"http://arxiv.org/pdf/2103.01934","source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"preprint"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3460278262","display_name":null,"funder_award_id":"AA4-2","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5280056699","display_name":null,"funder_award_id":"GRK 2433","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8671857726","display_name":null,"funder_award_id":"SPP 1886","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320324094","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3135196308.pdf","grobid_xml":"https://content.openalex.org/works/W3135196308.grobid-xml"},"referenced_works_count":57,"referenced_works":["https://openalex.org/W50417968","https://openalex.org/W79554687","https://openalex.org/W1602773783","https://openalex.org/W1604311391","https://openalex.org/W1804110266","https://openalex.org/W1841486359","https://openalex.org/W1993482030","https://openalex.org/W1995406764","https://openalex.org/W2001518794","https://openalex.org/W2031216664","https://openalex.org/W2036133196","https://openalex.org/W2036604884","https://openalex.org/W2081962379","https://openalex.org/W2088025933","https://openalex.org/W2094199988","https://openalex.org/W2126311658","https://openalex.org/W2137824542","https://openalex.org/W2171630320","https://openalex.org/W2181385834","https://openalex.org/W2226462370","https://openalex.org/W2336109516","https://openalex.org/W2343408237","https://openalex.org/W2479534775","https://openalex.org/W2515829451","https://openalex.org/W2550316793","https://openalex.org/W2620901441","https://openalex.org/W2736093993","https://openalex.org/W2750460732","https://openalex.org/W2778108844","https://openalex.org/W2793914895","https://openalex.org/W2895471748","https://openalex.org/W2918307016","https://openalex.org/W2963116674","https://openalex.org/W2963615834","https://openalex.org/W2965485141","https://openalex.org/W2970843715","https://openalex.org/W2986878057","https://openalex.org/W2997188511","https://openalex.org/W3014181683","https://openalex.org/W3021131124","https://openalex.org/W3035965352","https://openalex.org/W3037484550","https://openalex.org/W3041812180","https://openalex.org/W3043483664","https://openalex.org/W3085015010","https://openalex.org/W3092417881","https://openalex.org/W3099878876","https://openalex.org/W3103239355","https://openalex.org/W3110082550","https://openalex.org/W3123753597","https://openalex.org/W3124696154","https://openalex.org/W3134454852","https://openalex.org/W3162644644","https://openalex.org/W3176021757","https://openalex.org/W4205293427","https://openalex.org/W4231211112","https://openalex.org/W4300437123"],"related_works":["https://openalex.org/W3114815494","https://openalex.org/W4287549300","https://openalex.org/W2308319479","https://openalex.org/W2408949929","https://openalex.org/W2785696775","https://openalex.org/W4380354347","https://openalex.org/W3125976968","https://openalex.org/W2116066518","https://openalex.org/W3208440232","https://openalex.org/W2367757735"],"abstract_inverted_index":{"An":[0],"efficient":[1],"compression":[2],"technique":[3],"based":[4,104],"on":[5],"hierarchical":[6],"tensors":[7],"for":[8,26,55],"popular":[9],"option":[10,31],"pricing":[11],"methods":[12],"is":[13,16],"presented.":[14],"It":[15],"shown":[17],"that":[18],"the":[19,27,34,42,75,79,86,90],"\"curse":[20],"of":[21,29,62,74,89],"dimensionality\"":[22],"can":[23],"be":[24],"alleviated":[25],"computation":[28],"Bermudan":[30],"prices":[32],"with":[33],"Monte":[35],"Carlo":[36],"least-squares":[37],"approach":[38],"as":[39,41,69,71],"well":[40,70],"dual":[43],"martingale":[44],"method,":[45],"both":[46],"using":[47],"high-dimensional":[48],"tensorized":[49],"polynomial":[50],"expansions.":[51],"This":[52],"discretization":[53],"allows":[54],"a":[56,72],"simple":[57],"and":[58],"computationally":[59],"cheap":[60],"evaluation":[61],"conditional":[63],"expectations.":[64],"Complexity":[65],"estimates":[66],"are":[67],"provided":[68],"description":[73],"optimization":[76],"procedures":[77],"in":[78],"tensor":[80],"train":[81],"format.":[82],"Numerical":[83],"experiments":[84],"illustrate":[85],"favourable":[87],"accuracy":[88],"proposed":[91],"methods.":[92,105],"The":[93],"dynamical":[94],"programming":[95],"method":[96],"yields":[97],"results":[98],"comparable":[99],"to":[100],"recent":[101],"Neural":[102],"Network":[103]},"counts_by_year":[{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}