{"id":"https://openalex.org/W2133829578","doi":"https://doi.org/10.1137/040616267","title":"Retrieving L\u00e9vy Processes from Option Prices: Regularization of an Ill-posed Inverse Problem","display_name":"Retrieving L\u00e9vy Processes from Option Prices: Regularization of an Ill-posed Inverse Problem","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2133829578","doi":"https://doi.org/10.1137/040616267","mag":"2133829578"},"language":"en","primary_location":{"id":"doi:10.1137/040616267","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040616267","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/A5079973309","display_name":"Rama Cont","orcid":"https://orcid.org/0000-0003-1164-6053"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Rama Cont","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5052828075","display_name":"Peter Tankov","orcid":"https://orcid.org/0000-0003-4882-9806"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peter Tankov","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5079973309"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":11.0752,"has_fulltext":false,"cited_by_count":75,"citation_normalized_percentile":{"value":0.9824958,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"45","issue":"1","first_page":"1","last_page":"25"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.7578999996185303,"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":0.7578999996185303,"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":0.03400000184774399,"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.01769999973475933,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8304402828216553},{"id":"https://openalex.org/keywords/well-posed-problem","display_name":"Well-posed problem","score":0.6530521512031555},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.593631386756897},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.5928424596786499},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5480272769927979},{"id":"https://openalex.org/keywords/valuation-of-options","display_name":"Valuation of options","score":0.5243250131607056},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5228224992752075},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.45855942368507385},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42562949657440186},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.42324894666671753},{"id":"https://openalex.org/keywords/kullback\u2013leibler-divergence","display_name":"Kullback\u2013Leibler divergence","score":0.41101136803627014},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1995324194431305},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.1887846291065216},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12068885564804077},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08668655157089233}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8304402828216553},{"id":"https://openalex.org/C106214006","wikidata":"https://www.wikidata.org/wiki/Q1455898","display_name":"Well-posed problem","level":2,"score":0.6530521512031555},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.593631386756897},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5928424596786499},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5480272769927979},{"id":"https://openalex.org/C194483076","wikidata":"https://www.wikidata.org/wiki/Q380382","display_name":"Valuation of options","level":2,"score":0.5243250131607056},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5228224992752075},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.45855942368507385},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42562949657440186},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.42324894666671753},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.41101136803627014},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1995324194431305},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.1887846291065216},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12068885564804077},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08668655157089233},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/040616267","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040616267","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.155.662","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.155.662","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.ccsd.cnrs.fr/docs/00/00/33/57/PDF/ContTankov04.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.163.9120","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.163.9120","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.newton.cam.ac.uk/preprints/NI05014.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.74.1924","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.74.1924","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cmap.polytechnique.fr/~rama/papers/regularization.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1480459000","https://openalex.org/W1550925745","https://openalex.org/W1681010154","https://openalex.org/W1993516115","https://openalex.org/W2017392078","https://openalex.org/W2030354114","https://openalex.org/W2035197597","https://openalex.org/W2041550349","https://openalex.org/W2058903005","https://openalex.org/W2063819119","https://openalex.org/W2067367544","https://openalex.org/W2081774672","https://openalex.org/W2082028133","https://openalex.org/W2084764062","https://openalex.org/W2100630492","https://openalex.org/W2105832006","https://openalex.org/W2106154424","https://openalex.org/W2142278738","https://openalex.org/W2160709761","https://openalex.org/W2161007682","https://openalex.org/W2460254899","https://openalex.org/W2621596310","https://openalex.org/W3121405566","https://openalex.org/W3121900390","https://openalex.org/W3122895457","https://openalex.org/W3124062437","https://openalex.org/W3124475197","https://openalex.org/W4230395928"],"related_works":["https://openalex.org/W2385696774","https://openalex.org/W2386535317","https://openalex.org/W2542120579","https://openalex.org/W2761832462","https://openalex.org/W1947575127","https://openalex.org/W3187028418","https://openalex.org/W2167744125","https://openalex.org/W2024067282","https://openalex.org/W2520277554","https://openalex.org/W2068165956"],"abstract_inverted_index":{"Abstract.":[0],"We":[1,80],"propose":[2],"a":[3,19,75],"stable":[4,104],"nonparametric":[5],"method":[6],"for":[7,86],"constructing":[8],"an":[9,56],"option":[10,24],"pricing":[11,66],"model":[12,59],"of":[13,23,30,37,54,64,84,110,120],"exponential":[14,57,77],"L\u00e9vy":[15,58,78],"type,":[16],"consistent":[17],"with":[18,72,99,105],"given":[20],"data":[21,130],"set":[22],"prices.":[25],"After":[26],"demonstrating":[27],"the":[28,31,45,52,62,65,69,82,87,102,108,115,121,125,129],"ill-posedness":[29],"usual":[32],"and":[33,68,90,112],"least":[34,117],"squares":[35,118],"version":[36],"this":[38],"inverse":[39],"problem,":[40],"we":[41],"suggest":[42],"to":[43,74,101,107,114],"regularize":[44],"calibration":[46],"problem":[47,53,89,123],"by":[48],"reformulating":[49],"it":[50,93],"as":[51],"finding":[55],"that":[60,92],"minimizes":[61],"sum":[63],"error":[67],"relative":[70],"entropy":[71],"respect":[73,100,106],"prior":[76,111],"model.":[79],"prove":[81],"existence":[83],"solutions":[85,95],"regularized":[88],"show":[91],"yields":[94],"which":[96],"are":[97],"continuous":[98],"data,":[103],"choice":[109],"converge":[113],"minimum-entropy":[116],"solution":[119],"initial":[122],"when":[124],"noise":[126],"level":[127],"in":[128],"vanishes.":[131]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":12}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
