{"id":"https://openalex.org/W2588198751","doi":"https://doi.org/10.1137/15m1033502","title":"Solvable Diffusion Models with Linear and Mean-Reverting Nonlinear Drifts","display_name":"Solvable Diffusion Models with Linear and Mean-Reverting Nonlinear Drifts","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2588198751","doi":"https://doi.org/10.1137/15m1033502","mag":"2588198751"},"language":"en","primary_location":{"id":"doi:10.1137/15m1033502","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1033502","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071591774","display_name":"Giuseppe Campolieti","orcid":"https://orcid.org/0000-0002-6316-7313"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Giuseppe Campolieti","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5068968226","display_name":"Roman N. Makarov","orcid":"https://orcid.org/0000-0002-0935-9445"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Roman N. Makarov","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.687,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.73604042,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"8","issue":"1","first_page":"146","last_page":"170"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9362999796867371,"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":0.7578867673873901},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5832334756851196},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5425915718078613},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5370468497276306},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5314947962760925},{"id":"https://openalex.org/keywords/bessel-function","display_name":"Bessel function","score":0.48626601696014404},{"id":"https://openalex.org/keywords/conditional-expectation","display_name":"Conditional expectation","score":0.4762014150619507},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.4569537937641144},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.44002461433410645},{"id":"https://openalex.org/keywords/bessel-process","display_name":"Bessel process","score":0.43119633197784424},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.381062775850296},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2246294617652893},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.14891958236694336},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.14644676446914673},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10609984397888184}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7578867673873901},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5832334756851196},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5425915718078613},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5370468497276306},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5314947962760925},{"id":"https://openalex.org/C107706756","wikidata":"https://www.wikidata.org/wiki/Q219637","display_name":"Bessel function","level":2,"score":0.48626601696014404},{"id":"https://openalex.org/C186215838","wikidata":"https://www.wikidata.org/wiki/Q772232","display_name":"Conditional expectation","level":2,"score":0.4762014150619507},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.4569537937641144},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44002461433410645},{"id":"https://openalex.org/C118532472","wikidata":"https://www.wikidata.org/wiki/Q4896405","display_name":"Bessel process","level":5,"score":0.43119633197784424},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.381062775850296},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2246294617652893},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.14891958236694336},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.14644676446914673},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10609984397888184},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C78540521","wikidata":"https://www.wikidata.org/wiki/Q1498246","display_name":"Gegenbauer polynomials","level":4,"score":0.0},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/15m1033502","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1033502","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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/17","display_name":"Partnerships for the goals","score":0.550000011920929}],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1592561576","https://openalex.org/W1973387674","https://openalex.org/W2006789085","https://openalex.org/W2012772268","https://openalex.org/W2024493546","https://openalex.org/W2040934032","https://openalex.org/W2065581705","https://openalex.org/W2099793575","https://openalex.org/W2101346572","https://openalex.org/W2962937646","https://openalex.org/W3125409670"],"related_works":["https://openalex.org/W2962847248","https://openalex.org/W2073673068","https://openalex.org/W2136724503","https://openalex.org/W2951304618","https://openalex.org/W2108910538","https://openalex.org/W3099070185","https://openalex.org/W2008732497","https://openalex.org/W4297909333","https://openalex.org/W1605098306","https://openalex.org/W4250243911"],"abstract_inverted_index":{"We":[0,260],"present":[1,177],"new":[2,66,144,182,240],"extensions":[3],"to":[4,65,152,250,268,282,295],"a":[5,33,45,55,59,102,239,255],"method":[6,42],"for":[7,98,127,180,229,244],"constructing":[8],"families":[9,183],"of":[10,36,101,115,141,168,172,184,207,214,221,232,254,293],"solvable":[11,68,215],"one-dimensional":[12],"time-homogeneous":[13],"diffusions":[14,69,142,223],"whose":[15],"transition":[16],"densities":[17],"and":[18,54,120,130,149,155,196,224,284,308],"other":[19,156],"related":[20],"quantities":[21],"are":[22,71,147,150],"obtainable":[23],"in":[24,135,263],"analytically":[25],"closed":[26],"form.":[27],"Our":[28],"approach":[29],"is":[30,79,125],"based":[31],"on":[32],"dual":[34],"application":[35],"the":[37,77,94,138,169,189,197,204,218,245,251,266,290],"so-called":[38],"diffusion":[39,90,105,199],"canonical":[40],"transformation":[41],"that":[43,70,146,186],"combines":[44],"smooth":[46],"monotonic":[47],"differentiable":[48],"map":[49],"with":[50,86,107,248,276,280],"nonzero":[51],"derivative":[52],"(diffeomorphism)":[53],"measure":[56],"change":[57],"via":[58],"Doob-$h$":[60],"transform.":[61],"This":[62],"gives":[63],"rise":[64],"multiparameter":[67],"divided":[72],"into":[73],"two":[74,181],"main":[75],"classes;":[76],"first":[78,113,170],"specified":[80],"by":[81],"having":[82,117],"affine":[83,173],"(linear)":[84],"drift":[85,110,119,174,209],"various":[87],"resulting":[88,108],"nonlinear":[89,109,121,208],"coefficient":[91,106],"functions,":[92,124],"while":[93,137],"second":[95,139,205],"class":[96,114,140,171,206],"allows":[97],"several":[99,306],"specifications":[100],"(generally":[103],"nonlinear)":[104],"function.":[111],"The":[112],"models,":[116,175,210],"linear":[118],"(state-dependent)":[122],"volatility":[123,161,303],"useful":[126],"pricing":[128,153],"equity":[129],"foreign":[131],"exchange":[132],"(FX)":[133],"options":[134],"finance,":[136],"contains":[143],"models":[145,185,294],"mean-reverting":[148,222],"applicable":[151],"interest-rate":[154],"path-dependent":[157],"derivatives":[158],"such":[159],"as":[160],"index":[162],"(VIX)":[163],"options.":[164],"As":[165],"specific":[166],"examples":[167,213],"we":[176,211,237,287],"explicit":[178],"results":[179],"arise":[187],"from":[188],"squared":[190],"Bessel":[191,194,219],"process":[192],"(the":[193,200],"family)":[195],"Ornstein--Uhlenbeck":[198],"OU":[201,291],"family).":[202],"For":[203],"give":[212],"subfamilies":[216],"called":[217],"family":[220,292],"derive":[225,238],"closed-form":[226,241],"integral":[227],"formulas":[228],"conditional":[230],"expectations":[231],"certain":[233],"functionals.":[234],"In":[235],"particular,":[236],"analytical":[242],"formula":[243],"Laplace":[246,264],"transform":[247],"respect":[249,281],"strike":[252,283],"price":[253],"standard":[256],"call":[257,273],"VIX":[258,272],"option.":[259],"then":[261],"succeed":[262],"inverting":[265],"expression":[267],"obtain":[269],"numerically":[270],"exact":[271],"option":[274,297],"prices":[275],"realistic":[277],"implied":[278,302],"volatilities":[279],"maturity.":[285],"Moreover,":[286],"accurately":[288],"calibrate":[289],"FX":[296],"market":[298],"data,":[299],"exhibiting":[300],"pronounced":[301],"smiles":[304],"across":[305],"strikes":[307],"maturities.":[309]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2018,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}