{"id":"https://openalex.org/W407042200","doi":"https://doi.org/10.1007/978-1-4612-1784-8_36","title":"Optimal Portfolio Management with Partial Observations and Power Utility Function","display_name":"Optimal Portfolio Management with Partial Observations and Power Utility Function","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W407042200","doi":"https://doi.org/10.1007/978-1-4612-1784-8_36","mag":"407042200"},"language":"en","primary_location":{"id":"doi:10.1007/978-1-4612-1784-8_36","doi":"https://doi.org/10.1007/978-1-4612-1784-8_36","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-1-4612-1784-8_36","pdf_url":null,"source":{"id":"https://openalex.org/S4306462921","display_name":"Birkh\u00e4user Boston eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Stochastic Analysis, Control, Optimization and Applications","raw_type":"book-chapter"},"volume":{"id":"https://openalex.org/W2495854005","display_name":"Stochastic Analysis, Control, Optimization and Applications"},"type":"book-chapter","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/A5074272089","display_name":"Raymond Rishel","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Raymond Rishel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5074272089"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2771,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.86305732,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"605","last_page":"619"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9603999853134155,"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":0.9603999853134155,"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":0.036400001496076584,"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/T10047","display_name":"Financial Markets and Investment Strategies","score":0.0007999999797903001,"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/incomplete-information","display_name":"incomplete information","score":0.7580000162124634},{"id":"https://openalex.org/keywords/electricity-sector","display_name":"electric utilities","score":0.9259999990463257},{"id":"https://openalex.org/keywords/stock-price-models","display_name":"stock price modeling","score":0.6520000100135803},{"id":"https://openalex.org/keywords/geometric-brownian-motion","display_name":"geometric Brownian motion","score":0.9490000009536743},{"id":"https://openalex.org/keywords/bull-and-bear-markets","display_name":"bull and bear markets","score":0.9110000133514404},{"id":"https://openalex.org/keywords/stochastic-differential-equations","display_name":"stochastic differential equations","score":0.5299999713897705}],"concepts":[{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.6009350419044495},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5617464184761047},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.5518600940704346},{"id":"https://openalex.org/C101615488","wikidata":"https://www.wikidata.org/wiki/Q1503307","display_name":"Geometric Brownian motion","level":4,"score":0.5372934341430664},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.4536062180995941},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.4431791305541992},{"id":"https://openalex.org/C204036174","wikidata":"https://www.wikidata.org/wiki/Q909380","display_name":"Stock (firearms)","level":2,"score":0.4431120753288269},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.32893306016921997},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31183522939682007},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2579607367515564},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2578662037849426},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.22543811798095703},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.21175888180732727},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07343864440917969},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C136264566","wikidata":"https://www.wikidata.org/wiki/Q159810","display_name":"Economy","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C2780378061","wikidata":"https://www.wikidata.org/wiki/Q25351891","display_name":"Service (business)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-1-4612-1784-8_36","doi":"https://doi.org/10.1007/978-1-4612-1784-8_36","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-1-4612-1784-8_36","pdf_url":null,"source":{"id":"https://openalex.org/S4306462921","display_name":"Birkh\u00e4user Boston eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Stochastic Analysis, Control, Optimization and Applications","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1567262822","https://openalex.org/W1990330412","https://openalex.org/W2035168490","https://openalex.org/W2037704244","https://openalex.org/W2098612888","https://openalex.org/W2110607806","https://openalex.org/W4302609762","https://openalex.org/W7027865694"],"related_works":["https://openalex.org/W2622758503","https://openalex.org/W1970495888","https://openalex.org/W2352136706","https://openalex.org/W2605495741","https://openalex.org/W2334202328","https://openalex.org/W2051614088","https://openalex.org/W1987687311","https://openalex.org/W2998568909","https://openalex.org/W2013326494","https://openalex.org/W2203980050"],"abstract_inverted_index":{"A":[0,151],"common":[1],"model":[2,65,152,170,190],"for":[3,153,217,225],"a":[4,11,21,24,54,154,167,178,185,212,223,237,252],"stock":[5,22,71,129,155,219],"price":[6,18,156],"is":[7,10,16,53,166,177,183,197,211,222,228,243],"that":[8],"it":[9],"\u201cgeometric":[12],"Brownian":[13,55,179],"motion\u201d.":[14],"That":[15],"the":[17,29,66,70,91,98,108,124,128,138,172,191,202,218],"s(t)":[19],"of":[20,28,69,127,134,161,171],"satisfies":[23],"stochastic":[25,73,169],"differential":[26,74],"equation":[27],"type":[30],"(1)":[31],"$$":[32,49,76,85,111,120],"ds\\left(":[33],"t":[34,38,46,83,118],"\\right)":[35,48,84,119],"=":[36],"s\\left(":[37],"\\right)\\left(":[39],"{\\bar":[40],"r\\,dt\\,":[41],"+":[42,79,114],"\\,\\sigma":[43],"d\\beta":[44,81],"\\left(":[45,82,117],"\\right)}":[47],"in":[50,174],"which":[51,157,175,226],"\u03b1(t)":[52],"motion":[56,180],"process":[57,109],"and":[58,59,96,148,163,181,220],"\u03c3":[60],"are":[61],"constants.":[62],"For":[63,188],"this":[64,103,189,208,232,247],"growth":[67,94,105,125,194,215],"rate":[68,95,126,195,216],"has":[72,121,137],"(2)":[75],"\\bar":[77,112],"r\\,dt":[78],"\\sigma":[80,115],"with":[86],"$$\\bar":[87],"r$$":[88],"dt":[89],"being":[90],"infinitesmal":[92,99,192],"mean":[93,104,193,214],"\u03c3d\u00df(t)":[97],"random":[100,186,198,203],"fluctuations":[101,204],"about":[102,207],"rate.":[106],"Since":[107],"(3)":[110],"rt":[113],"\\beta":[116],"stationary":[122],"increments,":[123],"over":[130],"any":[131],"two":[132],"periods":[133],"equal":[135],"length":[136],"same":[139],"statistical":[140],"properties.":[141],"This":[142],"appears":[143],"to":[144],"rule":[145],"out":[146],"bull":[147,162,238],"bear":[149,164,253],"markets.":[150],"can":[158],"have":[159],"features":[160],"markets":[165],"doubly":[168],"form":[173],"\u00df(t)":[176,206],"r(t)":[182,227,242],"also":[184],"process.":[187],"r(t)dt":[196],"as":[199,201,236,251],"well":[200],"ad":[205],"mean.":[209],"If":[210],"target":[213],"there":[221],"period":[224],"substantially":[229,244],"larger":[230],"than":[231,246],"could":[233,248],"be":[234,249],"considered":[235,250],"market.":[239,254],"Conversely":[240],"when":[241],"less":[245]},"counts_by_year":[{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-10-10T09:11:00.788812","created_date":"2016-06-24T00:00:00"}