{"id":"https://openalex.org/W7223667054","doi":"https://doi.org/10.48550/arxiv.2610.32970","title":"On the continuity of conditional distributions and stratification for derivative pricing","display_name":"On the continuity of conditional distributions and stratification for derivative pricing","publication_year":2026,"publication_date":"2026-10-23","ids":{"openalex":"https://openalex.org/W7223667054","doi":"https://doi.org/10.48550/arxiv.2610.32970"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.32970","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.32970","pdf_url":"https://arxiv.org/pdf/2610.32970","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","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.32970","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069722300","display_name":"Aleksandar Arandjelovi\u0107","orcid":"https://orcid.org/0000-0003-2949-4860","observed_orcids":["https://orcid.org/0000-0003-2949-4860"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Arandjelovic, Aleksandar","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5002005113","display_name":"Patrick Cheridito","orcid":"https://orcid.org/0000-0001-9074-7295","observed_orcids":["https://orcid.org/0000-0001-9074-7295"]},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Cheridito, Patrick","raw_affiliation_strings":["Department of Mathematics , ETH Z\u00fcrich , Z\u00fcrich , Switzerland, and","Department of Mathematics , ETH Z\u00fcrich , Z\u00fcrich , Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , ETH Z\u00fcrich , Z\u00fcrich , Switzerland, and","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"Department of Mathematics , ETH Z\u00fcrich , Z\u00fcrich , Switzerland","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"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":0.9990000128746033,"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":0.9990000128746033,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/stratification","display_name":"stratification","score":0.7020000219345093},{"id":"https://openalex.org/keywords/derivatives-pricing","display_name":"derivative pricing","score":0.7429999709129333},{"id":"https://openalex.org/keywords/neural-network","display_name":"artificial neural networks","score":0.6830000281333923},{"id":"https://openalex.org/keywords/conditional-distributions","display_name":"conditional distributions","score":0.5379999876022339},{"id":"https://openalex.org/keywords/variance-reduction","display_name":"variance reduction","score":0.8009999990463257},{"id":"https://openalex.org/keywords/monte-carlo-simulation","display_name":"Monte Carlo simulation","score":0.8709999918937683},{"id":"https://openalex.org/keywords/proportional-allocation","display_name":"proportional allocation","score":0.6650000214576721},{"id":"https://openalex.org/keywords/universal-approximation-theorem","display_name":"universal approximation theorem","score":0.8370000123977661},{"id":"https://openalex.org/keywords/path-dependent-options","display_name":"path-dependent options","score":0.6600000262260437},{"id":"https://openalex.org/keywords/continuous-time-models","display_name":"continuous-time models","score":0.6420000195503235},{"id":"https://openalex.org/keywords/short-rate-models","display_name":"short rate models","score":0.7210000157356262}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6858999729156494},{"id":"https://openalex.org/C192943249","wikidata":"https://www.wikidata.org/wiki/Q1893382","display_name":"Stratification (seeds)","level":5,"score":0.5633999705314636},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5611000061035156},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.5189999938011169},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47360000014305115},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.43059998750686646},{"id":"https://openalex.org/C186215838","wikidata":"https://www.wikidata.org/wiki/Q772232","display_name":"Conditional expectation","level":2,"score":0.4302999973297119},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.4023999869823456},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.39480000734329224},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38940000534057617},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.38929998874664307},{"id":"https://openalex.org/C194483076","wikidata":"https://www.wikidata.org/wiki/Q380382","display_name":"Valuation of options","level":2,"score":0.3846000134944916},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.361299991607666},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.3515999913215637},{"id":"https://openalex.org/C43555835","wikidata":"https://www.wikidata.org/wiki/Q2300258","display_name":"Conditional probability distribution","level":2,"score":0.3483999967575073},{"id":"https://openalex.org/C186027771","wikidata":"https://www.wikidata.org/wiki/Q4008379","display_name":"Valuation (finance)","level":2,"score":0.33559998869895935},{"id":"https://openalex.org/C21430997","wikidata":"https://www.wikidata.org/wiki/Q5159279","display_name":"Conditional variance","level":4,"score":0.3222000002861023},{"id":"https://openalex.org/C85393063","wikidata":"https://www.wikidata.org/wiki/Q596307","display_name":"Stochastic volatility","level":3,"score":0.30079999566078186},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.2858000099658966},{"id":"https://openalex.org/C100279318","wikidata":"https://www.wikidata.org/wiki/Q467440","display_name":"Sample space","level":2,"score":0.2838999927043915},{"id":"https://openalex.org/C30084815","wikidata":"https://www.wikidata.org/wiki/Q4390268","display_name":"Variance-gamma distribution","level":4,"score":0.2806999981403351},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.2777999937534332},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2703999876976013},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.2623000144958496},{"id":"https://openalex.org/C93373587","wikidata":"https://www.wikidata.org/wiki/Q335632","display_name":"Mathematical finance","level":2,"score":0.26109999418258667},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.2540999948978424},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.2524000108242035}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.32970","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.32970","pdf_url":"https://arxiv.org/pdf/2610.32970","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.2610.32970","doi":"https://doi.org/10.48550/arxiv.2610.32970","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.32970","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:2610.32970","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.32970","pdf_url":"https://arxiv.org/pdf/2610.32970","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223667054.pdf","grobid_xml":"https://content.openalex.org/works/W7223667054.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4404224013","https://openalex.org/W3121624243","https://openalex.org/W2089969954","https://openalex.org/W2959813831","https://openalex.org/W4412040908","https://openalex.org/W2149372432","https://openalex.org/W7207859655","https://openalex.org/W2305704813","https://openalex.org/W1925448229","https://openalex.org/W2413747182"],"abstract_inverted_index":{"Stratification":[0],"can":[1],"reduce":[2],"the":[3,12,24,32,47,50,92,108,123,137,188],"estimator":[4],"variance":[5],"in":[6,37,62,80,84,104,171,181],"Monte":[7],"Carlo":[8],"simulations":[9],"by":[10],"partitioning":[11],"sample":[13],"space":[14],"according":[15],"to":[16,31,60],"a":[17,69,112,153,167,172,178,182],"low-dimensional":[18,55],"factor":[19,114],"and":[20,53,76,132,177],"sampling":[21],"separately":[22],"within":[23],"resulting":[25],"strata,":[26],"making":[27],"it":[28],"well":[29],"suited":[30],"valuation":[33],"of":[34,49,94,111,139],"path-dependent":[35],"claims":[36],"high-dimensional":[38],"financial":[39],"models.":[40,65,106],"Its":[41],"performance,":[42],"however,":[43],"depends":[44],"critically":[45],"on":[46],"choice":[48],"stratification":[51,96,113,159],"factor,":[52],"effective":[54],"factors":[56,97,190],"are":[57],"generally":[58],"difficult":[59],"identify":[61],"complex":[63],"continuous-time":[64,105],"Neural":[66],"networks":[67],"provide":[68,133],"flexible":[70],"approximation":[71,155],"class":[72],"for":[73,98,122,147,157],"this":[74,88,140],"purpose":[75],"have":[77],"proved":[78],"useful":[79],"related":[81],"variance-reduction":[82],"problems":[83],"quantitative":[85],"finance.":[86],"In":[87],"paper,":[89],"we":[90,118],"study":[91],"construction":[93,110],"neural":[95,148],"derivative":[99],"pricing":[100],"under":[101],"proportional":[102],"allocation":[103],"Since":[107],"numerical":[109,164],"typically":[115],"involves":[116],"approximation,":[117],"establish":[119],"continuity":[120,141],"results":[121,146],"associated":[124],"conditional":[125,130],"expectations":[126],"and,":[127],"more":[128],"generally,":[129],"distributions,":[131],"several":[134],"counterexamples":[135],"showing":[136],"limits":[138],"theory.":[142],"Combined":[143],"with":[144,163],"density":[145],"networks,":[149],"our":[150],"findings":[151],"yield":[152],"universal":[154],"theorem":[156],"admissible":[158],"factors.":[160],"We":[161],"conclude":[162],"experiments":[165],"involving":[166],"constant-maturity-swap":[168],"range":[169],"accrual":[170],"two-factor":[173],"Gaussian":[174],"short-rate":[175],"model":[176],"worst-of":[179],"autocallable":[180],"Wishart":[183],"stochastic":[184],"covariance":[185],"model,":[186],"where":[187],"learned":[189],"outperform":[191],"all":[192],"considered":[193],"benchmarks.":[194]},"counts_by_year":[],"updated_date":"2026-10-29T09:56:32.521200","created_date":"2026-10-27T00:00:00"}
