{"id":"https://openalex.org/W7224112863","doi":"https://doi.org/10.48550/arxiv.2610.36921","title":"A Deep Learning-Driven Operator Splitting Scheme for Free Boundary Problems: An Application to American Option Pricing in Incomplete Markets","display_name":"A Deep Learning-Driven Operator Splitting Scheme for Free Boundary Problems: An Application to American Option Pricing in Incomplete Markets","publication_year":2026,"publication_date":"2026-10-27","ids":{"openalex":"https://openalex.org/W7224112863","doi":"https://doi.org/10.48550/arxiv.2610.36921"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.36921","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.36921","pdf_url":"https://arxiv.org/pdf/2610.36921","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.36921","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080233678","display_name":"Dong Yan","orcid":"https://orcid.org/0000-0003-4549-9469","observed_orcids":["https://orcid.org/0000-0003-4549-9469"]},"institutions":[{"id":"https://openalex.org/I146563203","display_name":"University of International Business and Economics","ror":"https://ror.org/05khqpb71","country_code":"CN","type":"education","lineage":["https://openalex.org/I146563203"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yan, Dong","raw_affiliation_strings":["School of Statistics , University of International Business and Economics , Beijing , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Statistics , University of International Business and Economics , Beijing , China","institution_ids":["https://openalex.org/I146563203"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042538362","display_name":"Haocheng Zhu","orcid":"https://orcid.org/0009-0009-5862-4362","observed_orcids":["https://orcid.org/0009-0009-5862-4362","https://orcid.org/0009-0001-7159-6521"]},"institutions":[{"id":"https://openalex.org/I146563203","display_name":"University of International Business and Economics","ror":"https://ror.org/05khqpb71","country_code":"CN","type":"education","lineage":["https://openalex.org/I146563203"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhu, Haocheng","raw_affiliation_strings":["China School of Banking and Finance , University of International Business and Economics , Beijing , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"China School of Banking and Finance , University of International Business and Economics , Beijing , China","institution_ids":["https://openalex.org/I146563203"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5160027894","display_name":"Yao Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I204831749","display_name":"Southwestern University of Finance and Economics","ror":"https://ror.org/04ewct822","country_code":"CN","type":"education","lineage":["https://openalex.org/I204831749"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li, Yao","raw_affiliation_strings":["School of Mathematics , Southwestern University of Finance and Economics , Chengdu , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics , Southwestern University of Finance and Economics , Chengdu , China","institution_ids":["https://openalex.org/I204831749"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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":0.9810000061988831,"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":0.9810000061988831,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.016100000590085983,"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/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/operator-splitting","display_name":"operator splitting","score":0.7269999980926514},{"id":"https://openalex.org/keywords/free-boundary-problem","display_name":"free boundary problem","score":0.9710000157356262},{"id":"https://openalex.org/keywords/american-option-pricing","display_name":"American option pricing","score":0.9629999995231628},{"id":"https://openalex.org/keywords/incomplete-markets","display_name":"incomplete markets","score":0.9610000252723694},{"id":"https://openalex.org/keywords/variational-inequalities","display_name":"variational inequalities","score":0.8009999990463257},{"id":"https://openalex.org/keywords/physics-informed-neural-networks","display_name":"physics-informed neural networks","score":0.9750000238418579},{"id":"https://openalex.org/keywords/nonlinear-drift","display_name":"nonlinear drift","score":0.7289999723434448},{"id":"https://openalex.org/keywords/transaction-costs","display_name":"transaction costs","score":0.7519999742507935},{"id":"https://openalex.org/keywords/high-dimensional-pdes","display_name":"high-dimensional PDEs","score":0.7020000219345093}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6877999901771545},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.588699996471405},{"id":"https://openalex.org/C2777970221","wikidata":"https://www.wikidata.org/wiki/Q7049482","display_name":"Nonlinear pricing","level":2,"score":0.570900022983551},{"id":"https://openalex.org/C109354906","wikidata":"https://www.wikidata.org/wiki/Q6015174","display_name":"Incomplete markets","level":2,"score":0.5454000234603882},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5282999873161316},{"id":"https://openalex.org/C194483076","wikidata":"https://www.wikidata.org/wiki/Q380382","display_name":"Valuation of options","level":2,"score":0.5058000087738037},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.48989999294281006},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4778999984264374},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.46140000224113464},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4113999903202057},{"id":"https://openalex.org/C163128081","wikidata":"https://www.wikidata.org/wiki/Q1338307","display_name":"Black\u2013Scholes model","level":3,"score":0.4097999930381775},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3880000114440918},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.375900000333786},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.36899998784065247},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.3610999882221222},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.3522000014781952},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.35100001096725464},{"id":"https://openalex.org/C99414536","wikidata":"https://www.wikidata.org/wiki/Q7098950","display_name":"Optimal stopping","level":2,"score":0.31779998540878296},{"id":"https://openalex.org/C186215838","wikidata":"https://www.wikidata.org/wiki/Q772232","display_name":"Conditional expectation","level":2,"score":0.3100000023841858},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.2939999997615814},{"id":"https://openalex.org/C88731125","wikidata":"https://www.wikidata.org/wiki/Q7935676","display_name":"Viscosity solution","level":2,"score":0.2863999903202057},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.2827000021934509},{"id":"https://openalex.org/C196267783","wikidata":"https://www.wikidata.org/wiki/Q4392490","display_name":"Resolvent","level":2,"score":0.27900001406669617},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.27790001034736633},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.25859999656677246},{"id":"https://openalex.org/C2777600642","wikidata":"https://www.wikidata.org/wiki/Q1508707","display_name":"Call option","level":2,"score":0.25459998846054077},{"id":"https://openalex.org/C2778311368","wikidata":"https://www.wikidata.org/wiki/Q1939618","display_name":"Put option","level":2,"score":0.2533999979496002}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.36921","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.36921","pdf_url":"https://arxiv.org/pdf/2610.36921","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.2610.36921","doi":"https://doi.org/10.48550/arxiv.2610.36921","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.36921","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.36921","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.36921","pdf_url":"https://arxiv.org/pdf/2610.36921","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/W7224112863.pdf","grobid_xml":"https://content.openalex.org/works/W7224112863.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4386897094","https://openalex.org/W7105099652","https://openalex.org/W1995495346","https://openalex.org/W4231309816","https://openalex.org/W2077177053","https://openalex.org/W4393515331","https://openalex.org/W1982600291","https://openalex.org/W7215091274","https://openalex.org/W2288495973","https://openalex.org/W2337345461"],"abstract_inverted_index":{"This":[0],"paper":[1],"proposes":[2],"a":[3,18,22,28,54,78,83],"deep":[4],"learning-driven":[5],"operator":[6],"splitting":[7],"scheme":[8,62,105],"for":[9],"high-dimensional":[10],"free-boundary":[11],"problems,":[12],"with":[13,24,32,128,134],"American":[14],"option":[15,118],"pricing":[16,48],"as":[17],"representative":[19],"application.":[20],"In":[21],"market":[23],"proportional":[25],"transaction":[26],"costs,":[27],"stochastic":[29,45],"liquidity":[30],"risk":[31],"an":[33,72],"empirically":[34],"validated":[35,107],"nonlinear":[36,57],"drift":[37],"based":[38],"on":[39],"S&P":[40],"500":[41],"data,":[42],"and":[43,82,101,110,115,120],"two-factor":[44],"volatility,":[46],"the":[47,51,88,117,121,129,137],"problem":[49],"takes":[50],"form":[52],"of":[53],"five-dimensional":[55],"highly":[56],"variational":[58,65],"inequality.":[59],"The":[60,104],"proposed":[61],"decomposes":[63],"this":[64],"inequality":[66],"at":[67],"each":[68],"time":[69],"layer":[70],"into":[71],"elliptic":[73],"continuation":[74],"equation":[75],"approximated":[76],"by":[77],"physics-informed":[79],"neural":[80],"network":[81],"closed-form":[84],"projection":[85],"step":[86],"enforcing":[87],"early-exercise":[89],"constraint.":[90],"A":[91],"conditional":[92],"$\\ell^\\infty$":[93],"stability":[94],"bound":[95],"is":[96,106],"derived":[97],"under":[98],"stated":[99],"resolvent":[100],"Lipschitz":[102],"assumptions.":[103],"against":[108],"finite-difference":[109],"least-squares":[111],"Monte":[112],"Carlo":[113],"benchmarks,":[114],"both":[116],"prices":[119],"learned":[122],"exercise":[123],"boundary":[124],"show":[125],"close":[126],"agreement":[127],"reference":[130],"solutions.":[131],"Sensitivity":[132],"analyses":[133],"respect":[135],"to":[136],"key":[138],"model":[139],"parameters":[140],"are":[141],"also":[142],"reported.":[143]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-29T00:00:00"}