{"id":"https://openalex.org/W1990833943","doi":"https://doi.org/10.1137/09077878x","title":"Processes of Class Sigma, Last Passage Times, and Drawdowns","display_name":"Processes of Class Sigma, Last Passage Times, and Drawdowns","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1990833943","doi":"https://doi.org/10.1137/09077878x","mag":"1990833943"},"language":"en","primary_location":{"id":"doi:10.1137/09077878x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/09077878x","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/A5002005113","display_name":"Patrick Cheridito","orcid":"https://orcid.org/0000-0001-9074-7295"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Patrick Cheridito","raw_affiliation_strings":["Princeton University#TAB#"],"affiliations":[{"raw_affiliation_string":"Princeton University#TAB#","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024549033","display_name":"Ashkan Nikeghbali","orcid":"https://orcid.org/0000-0002-8161-7357"},"institutions":[{"id":"https://openalex.org/I202697423","display_name":"University of Zurich","ror":"https://ror.org/02crff812","country_code":"CH","type":"education","lineage":["https://openalex.org/I202697423"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Ashkan Nikeghbali","raw_affiliation_strings":["Institute of Mathematics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland","institution_ids":["https://openalex.org/I202697423"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080842355","display_name":"Eckhard Platen","orcid":"https://orcid.org/0000-0003-4595-3123"},"institutions":[{"id":"https://openalex.org/I114017466","display_name":"University of Technology Sydney","ror":"https://ror.org/03f0f6041","country_code":"AU","type":"education","lineage":["https://openalex.org/I114017466"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Eckhard Platen","raw_affiliation_strings":["School of Mathematical Sciences and Finance Discipline Group, University of Technology, Sydney, PO Box 123 Broadway, NSW 2007, Australia"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences and Finance Discipline Group, University of Technology, Sydney, PO Box 123 Broadway, NSW 2007, Australia","institution_ids":["https://openalex.org/I114017466"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5002005113"],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":null,"apc_paid":null,"fwci":4.6138,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.95049402,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"3","issue":"1","first_page":"280","last_page":"303"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9980000257492065,"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":0.9980000257492065,"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/T11720","display_name":"Probability and Risk Models","score":0.9973000288009644,"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"}},{"id":"https://openalex.org/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9886000156402588,"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":0.6405078172683716},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6225104331970215},{"id":"https://openalex.org/keywords/sigma","display_name":"Sigma","score":0.6034916639328003},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5553989410400391},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.5105680227279663},{"id":"https://openalex.org/keywords/maxima","display_name":"Maxima","score":0.4819640815258026},{"id":"https://openalex.org/keywords/l\u00e9vy-process","display_name":"L\u00e9vy process","score":0.44783639907836914},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4042559266090393},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.397136926651001},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20329001545906067},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.17084857821464539},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10008841753005981}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6405078172683716},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6225104331970215},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.6034916639328003},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5553989410400391},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.5105680227279663},{"id":"https://openalex.org/C91528185","wikidata":"https://www.wikidata.org/wiki/Q520952","display_name":"Maxima","level":3,"score":0.4819640815258026},{"id":"https://openalex.org/C88757350","wikidata":"https://www.wikidata.org/wiki/Q1557613","display_name":"L\u00e9vy process","level":2,"score":0.44783639907836914},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4042559266090393},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.397136926651001},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20329001545906067},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.17084857821464539},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10008841753005981},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C52119013","wikidata":"https://www.wikidata.org/wiki/Q50637","display_name":"Art history","level":1,"score":0.0},{"id":"https://openalex.org/C554144382","wikidata":"https://www.wikidata.org/wiki/Q213156","display_name":"Performance art","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/09077878x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/09077878x","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:uts:ppaper:2012-4","is_oa":false,"landing_page_url":"https://epubs.siam.org/doi/abs/10.1137/09077878X","pdf_url":null,"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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1958472221","display_name":"CAREER:  Quantification of Risk","funder_award_id":"0642361","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W195252046","https://openalex.org/W659329649","https://openalex.org/W1536374753","https://openalex.org/W1544189955","https://openalex.org/W1545370368","https://openalex.org/W1552064164","https://openalex.org/W1920130955","https://openalex.org/W1969689392","https://openalex.org/W1978466391","https://openalex.org/W1982381011","https://openalex.org/W1986490170","https://openalex.org/W1995522593","https://openalex.org/W1998428654","https://openalex.org/W2021163852","https://openalex.org/W2021305902","https://openalex.org/W2026044854","https://openalex.org/W2093669121","https://openalex.org/W2116136997","https://openalex.org/W2119657026","https://openalex.org/W2138566360","https://openalex.org/W2149286090","https://openalex.org/W2157390830","https://openalex.org/W2161269853","https://openalex.org/W2166720436","https://openalex.org/W2230483832","https://openalex.org/W2462232973","https://openalex.org/W2950850758","https://openalex.org/W2953290461","https://openalex.org/W3125796373"],"related_works":["https://openalex.org/W2901492383","https://openalex.org/W2901973005","https://openalex.org/W2055124383","https://openalex.org/W2913309527","https://openalex.org/W2159775375","https://openalex.org/W1841759989","https://openalex.org/W4308335705","https://openalex.org/W2130929518","https://openalex.org/W4236460739","https://openalex.org/W2950839898"],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,14,73,103,107,138,166,181,207],"general":[3,33,64],"framework":[4],"for":[5],"studying":[6],"last":[7,84,101,130],"passage":[8,131],"times,":[9],"suprema,":[10],"and":[11,30,57,82,148,218],"drawdowns":[12,220],"of":[13,17,27,35,39,54,72,75,99,129,155,177,190,193,195,206,209,221],"large":[15],"class":[16,28,76,196],"continuous-time":[18],"stochastic":[19,104,139],"processes.":[20,224],"Our":[21,133],"approach":[22],"is":[23,46,111,137],"based":[24],"on":[25,151],"processes":[26,56,194],"Sigma":[29,77],"the":[31,44,48,70,83,88,97,100,152,162,172,178,204],"more":[32],"concept":[34],"two":[36],"processes,":[37],"one":[38],"which":[40],"moves":[41],"only":[42],"when":[43,161,171],"other":[45],"at":[47],"origin.":[49,89],"After":[50],"investigating":[51],"certain":[52,108,191],"transformations":[53],"such":[55,213],"their":[58],"convergence":[59],"properties,":[60],"we":[61],"provide":[62],"three":[63],"representation":[65,135,141,186],"results.":[66],"The":[67,184],"first":[68],"allows":[69],"recovery":[71],"process":[74,105],"from":[78],"its":[79,114],"final":[80],"value":[81],"time":[85,102],"it":[86],"visited":[87],"In":[90],"many":[91],"situations":[92],"this":[93],"gives":[94,187],"access":[95],"to":[96,113,120,146,165,202],"distribution":[98],"attains":[106,180],"level":[109,168],"or":[110,174],"equal":[112],"running":[115,153,215],"maximum.":[116],"It":[117,198],"also":[118],"leads":[119],"recently":[121],"discovered":[122],"formulas":[123],"expressing":[124],"option":[125],"prices":[126],"in":[127],"terms":[128],"times.":[132],"second":[134],"result":[136],"integral":[140],"that":[142,158],"will":[143],"allow":[144],"us":[145],"price":[147],"hedge":[149],"options":[150],"maximum":[154,219],"an":[156],"underlying":[157,163,179],"are":[159],"triggered":[160],"drops":[164],"given":[167,182],"or,":[169],"alternatively,":[170],"drawdown":[173,176],"relative":[175],"height.":[183],"third":[185],"conditional":[188],"expectations":[189],"functionals":[192],"Sigma.":[197],"can":[199],"be":[200],"used":[201],"deduce":[203],"distributions":[205],"variety":[208],"interesting":[210],"random":[211],"variables":[212],"as":[214],"maxima,":[216],"drawdowns,":[217],"suitably":[222],"stopped":[223]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}