{"id":"https://openalex.org/W4401512592","doi":"https://doi.org/10.3390/axioms13080543","title":"Optimal Investment Strategy for DC Pension Plan with Stochastic Salary and Value at Risk Constraint in Stochastic Volatility Model","display_name":"Optimal Investment Strategy for DC Pension Plan with Stochastic Salary and Value at Risk Constraint in Stochastic Volatility Model","publication_year":2024,"publication_date":"2024-08-10","ids":{"openalex":"https://openalex.org/W4401512592","doi":"https://doi.org/10.3390/axioms13080543"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13080543","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13080543","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/axioms13080543","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041887039","display_name":"Zilan Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I149735164","display_name":"Hengyang Normal University","ror":"https://ror.org/006bvjm48","country_code":"CN","type":"education","lineage":["https://openalex.org/I149735164"]},{"id":"https://openalex.org/I173759888","display_name":"Hunan Normal University","ror":"https://ror.org/053w1zy07","country_code":"CN","type":"education","lineage":["https://openalex.org/I173759888"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zilan Liu","raw_affiliation_strings":["Faculty of Economics and Management, Hengyang Normal University, Hengyang 421002, China","School of Business, Hunan Normal University, Changsha 410081, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Economics and Management, Hengyang Normal University, Hengyang 421002, China","institution_ids":["https://openalex.org/I149735164"]},{"raw_affiliation_string":"School of Business, Hunan Normal University, Changsha 410081, China","institution_ids":["https://openalex.org/I173759888"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019121141","display_name":"Huanying Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I173759888","display_name":"Hunan Normal University","ror":"https://ror.org/053w1zy07","country_code":"CN","type":"education","lineage":["https://openalex.org/I173759888"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huanying Zhang","raw_affiliation_strings":["Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China","institution_ids":["https://openalex.org/I173759888"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100713695","display_name":"Yijun Wang","orcid":"https://orcid.org/0000-0002-8161-2150"},"institutions":[{"id":"https://openalex.org/I7726996","display_name":"Henan University of Economic and Law","ror":"https://ror.org/000jtc944","country_code":"CN","type":"education","lineage":["https://openalex.org/I7726996"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yijun Wang","raw_affiliation_strings":["School of Finance, Henan University of Economics and Law, Zhengzhou 450016, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Finance, Henan University of Economics and Law, Zhengzhou 450016, China","institution_ids":["https://openalex.org/I7726996"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101792439","display_name":"Ya Huang","orcid":"https://orcid.org/0000-0003-1101-6481"},"institutions":[{"id":"https://openalex.org/I173759888","display_name":"Hunan Normal University","ror":"https://ror.org/053w1zy07","country_code":"CN","type":"education","lineage":["https://openalex.org/I173759888"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ya Huang","raw_affiliation_strings":["School of Business, Hunan Normal University, Changsha 410081, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Business, Hunan Normal University, Changsha 410081, China","institution_ids":["https://openalex.org/I173759888"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100713695"],"corresponding_institution_ids":["https://openalex.org/I7726996"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":3.9644,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.93984707,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"13","issue":"8","first_page":"543","last_page":"543"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12011","display_name":"Insurance, Mortality, Demography, Risk Management","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/3317","display_name":"Demography"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T12011","display_name":"Insurance, Mortality, Demography, Risk Management","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/3317","display_name":"Demography"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9983999729156494,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.9983000159263611,"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/cvar","display_name":"CVAR","score":0.9198500514030457},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.5610679984092712},{"id":"https://openalex.org/keywords/stochastic-volatility","display_name":"Stochastic volatility","score":0.5596111416816711},{"id":"https://openalex.org/keywords/stochastic-programming","display_name":"Stochastic programming","score":0.5235761404037476},{"id":"https://openalex.org/keywords/geometric-brownian-motion","display_name":"Geometric Brownian motion","score":0.5097967982292175},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5034782290458679},{"id":"https://openalex.org/keywords/expected-shortfall","display_name":"Expected shortfall","score":0.49694111943244934},{"id":"https://openalex.org/keywords/volatility","display_name":"Volatility (finance)","score":0.46510156989097595},{"id":"https://openalex.org/keywords/value-at-risk","display_name":"Value at risk","score":0.46400776505470276},{"id":"https://openalex.org/keywords/stochastic-investment-model","display_name":"Stochastic investment model","score":0.4348521828651428},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.41105547547340393},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.3995027542114258},{"id":"https://openalex.org/keywords/risk-management","display_name":"Risk management","score":0.38619837164878845},{"id":"https://openalex.org/keywords/asset-allocation","display_name":"Asset allocation","score":0.36388880014419556},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.30269134044647217},{"id":"https://openalex.org/keywords/portfolio","display_name":"Portfolio","score":0.23965352773666382},{"id":"https://openalex.org/keywords/finance","display_name":"Finance","score":0.1962738037109375},{"id":"https://openalex.org/keywords/diffusion-process","display_name":"Diffusion process","score":0.15445297956466675}],"concepts":[{"id":"https://openalex.org/C2779922397","wikidata":"https://www.wikidata.org/wiki/Q5014755","display_name":"CVAR","level":4,"score":0.9198500514030457},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.5610679984092712},{"id":"https://openalex.org/C85393063","wikidata":"https://www.wikidata.org/wiki/Q596307","display_name":"Stochastic volatility","level":3,"score":0.5596111416816711},{"id":"https://openalex.org/C137631369","wikidata":"https://www.wikidata.org/wiki/Q7617831","display_name":"Stochastic programming","level":2,"score":0.5235761404037476},{"id":"https://openalex.org/C101615488","wikidata":"https://www.wikidata.org/wiki/Q1503307","display_name":"Geometric Brownian motion","level":4,"score":0.5097967982292175},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5034782290458679},{"id":"https://openalex.org/C5496284","wikidata":"https://www.wikidata.org/wiki/Q5420856","display_name":"Expected shortfall","level":3,"score":0.49694111943244934},{"id":"https://openalex.org/C91602232","wikidata":"https://www.wikidata.org/wiki/Q756115","display_name":"Volatility (finance)","level":2,"score":0.46510156989097595},{"id":"https://openalex.org/C94128290","wikidata":"https://www.wikidata.org/wiki/Q963287","display_name":"Value at risk","level":3,"score":0.46400776505470276},{"id":"https://openalex.org/C117219021","wikidata":"https://www.wikidata.org/wiki/Q7617821","display_name":"Stochastic investment model","level":4,"score":0.4348521828651428},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.41105547547340393},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3995027542114258},{"id":"https://openalex.org/C32896092","wikidata":"https://www.wikidata.org/wiki/Q189447","display_name":"Risk management","level":2,"score":0.38619837164878845},{"id":"https://openalex.org/C139819358","wikidata":"https://www.wikidata.org/wiki/Q462748","display_name":"Asset allocation","level":3,"score":0.36388880014419556},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30269134044647217},{"id":"https://openalex.org/C2780821815","wikidata":"https://www.wikidata.org/wiki/Q5340806","display_name":"Portfolio","level":2,"score":0.23965352773666382},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.1962738037109375},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.15445297956466675},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C2780378061","wikidata":"https://www.wikidata.org/wiki/Q25351891","display_name":"Service (business)","level":2,"score":0.0},{"id":"https://openalex.org/C136264566","wikidata":"https://www.wikidata.org/wiki/Q159810","display_name":"Economy","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms13080543","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13080543","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:c71bcbac4f4c4421a23ff58b809fadb8","is_oa":true,"landing_page_url":"https://doaj.org/article/c71bcbac4f4c4421a23ff58b809fadb8","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 13, Iss 8, p 543 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms13080543","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13080543","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.4099999964237213,"display_name":"Partnerships for the goals","id":"https://metadata.un.org/sdg/17"}],"awards":[{"id":"https://openalex.org/G1050125954","display_name":null,"funder_award_id":"23YJC910008","funder_id":"https://openalex.org/F4320335982","funder_display_name":"Humanities and Social Science Fund of Ministry of Education of China"},{"id":"https://openalex.org/G1343151889","display_name":null,"funder_award_id":"22BTJ058","funder_id":"https://openalex.org/F4320335869","funder_display_name":"National Social Science Fund of China"},{"id":"https://openalex.org/G1902074334","display_name":null,"funder_award_id":"2023JJ30381","funder_id":"https://openalex.org/F4320335869","funder_display_name":"National Social Science Fund of China"},{"id":"https://openalex.org/G2020372061","display_name":null,"funder_award_id":"kq2208159","funder_id":"https://openalex.org/F4320335982","funder_display_name":"Humanities and Social Science Fund of Ministry of Education of China"},{"id":"https://openalex.org/G2049355050","display_name":null,"funder_award_id":"22BTJ058","funder_id":"https://openalex.org/F4320335982","funder_display_name":"Humanities and Social Science Fund of Ministry of Education of China"},{"id":"https://openalex.org/G3217759207","display_name":null,"funder_award_id":"23AJY027","funder_id":"https://openalex.org/F4320335869","funder_display_name":"National Social Science Fund of China"},{"id":"https://openalex.org/G6042473234","display_name":null,"funder_award_id":"kq2208159","funder_id":"https://openalex.org/F4320335869","funder_display_name":"National Social Science Fund of China"},{"id":"https://openalex.org/G7337112738","display_name":null,"funder_award_id":"23YJC910008","funder_id":"https://openalex.org/F4320335869","funder_display_name":"National Social Science Fund of China"},{"id":"https://openalex.org/G8725899151","display_name":null,"funder_award_id":"2023JJ30381","funder_id":"https://openalex.org/F4320335982","funder_display_name":"Humanities and Social Science Fund of Ministry of Education of China"},{"id":"https://openalex.org/G8960237260","display_name":null,"funder_award_id":"23AJY027","funder_id":"https://openalex.org/F4320335982","funder_display_name":"Humanities and Social Science Fund of Ministry of Education of China"}],"funders":[{"id":"https://openalex.org/F4320335869","display_name":"National Social Science Fund of China","ror":null},{"id":"https://openalex.org/F4320335982","display_name":"Humanities and Social Science Fund of Ministry of Education of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W940111555","https://openalex.org/W1551720412","https://openalex.org/W1969948172","https://openalex.org/W1972115786","https://openalex.org/W1979933030","https://openalex.org/W2000640663","https://openalex.org/W2017465488","https://openalex.org/W2019291268","https://openalex.org/W2025582260","https://openalex.org/W2064561530","https://openalex.org/W2084889689","https://openalex.org/W2113155572","https://openalex.org/W2115814664","https://openalex.org/W2118856090","https://openalex.org/W2124640999","https://openalex.org/W2143299583","https://openalex.org/W2155511751","https://openalex.org/W2324161544","https://openalex.org/W2412841086","https://openalex.org/W2528992776","https://openalex.org/W2535549511","https://openalex.org/W2745548924","https://openalex.org/W2794305678","https://openalex.org/W2807750174","https://openalex.org/W2923188802","https://openalex.org/W2947349642","https://openalex.org/W3123079000","https://openalex.org/W3123552065","https://openalex.org/W3132556315","https://openalex.org/W3134531946","https://openalex.org/W3181498587","https://openalex.org/W4206587967","https://openalex.org/W4281558750","https://openalex.org/W4289986009","https://openalex.org/W4388297072","https://openalex.org/W4389670464","https://openalex.org/W4390031857"],"related_works":["https://openalex.org/W4316167276","https://openalex.org/W2002736235","https://openalex.org/W2232143283","https://openalex.org/W1647779468","https://openalex.org/W1106997938","https://openalex.org/W2783733712","https://openalex.org/W2594064876","https://openalex.org/W2374661407","https://openalex.org/W2031780815","https://openalex.org/W2047632359"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"the":[3,33,48,66,81,101,120,125,131,162,173],"optimal":[4,146,174],"asset":[5,39,43],"allocation":[6],"problem":[7],"of":[8,69,138,145,164],"a":[9,16,22,25,37,41,60,104,110,114,152,165],"defined":[10],"contribution":[11],"(DC)":[12],"pension":[13,83],"plan":[14],"with":[15,55,149],"stochastic":[17,26,50,93],"salary":[18,88],"and":[19,40,58,75,94,124,150,169],"value":[20],"under":[21,113],"constraint":[23,106,112,168],"within":[24],"volatility":[27,51],"model.":[28,52,86],"It":[29],"is":[30,89,107],"assumed":[31,90],"that":[32],"financial":[34],"market":[35],"contains":[36],"risk-free":[38],"risky":[42],"whose":[44],"price":[45],"process":[46],"satisfies":[47],"Stein\u2013Stein":[49],"To":[53],"comply":[54],"regulatory":[56],"standards":[57],"offer":[59],"risk":[61,134],"management":[62,85],"tool,":[63],"we":[64,141],"integrate":[65],"dynamic":[67,102,126,166],"versions":[68],"Value-at-Risk":[70,73],"(VaR),":[71],"Conditional":[72],"(CVaR),":[74],"worst-case":[76],"CVaR":[77],"(wcCVaR)":[78],"constraints":[79],"into":[80],"DC":[82],"fund":[84],"The":[87],"to":[91,109,129,160],"be":[92],"characterized":[95],"by":[96],"geometric":[97],"Brownian":[98],"motion.":[99],"In":[100],"setting,":[103],"CVaR/wcCVaR":[105],"equivalent":[108],"VaR":[111,153],"higher":[115],"confidence":[116],"level.":[117],"By":[118],"using":[119],"Lagrange":[121],"multiplier":[122],"method":[123,128],"programming":[127],"maximize":[130],"constant":[132],"absolute":[133],"aversion":[135],"(CARA)":[136],"utility":[137],"terminal":[139],"wealth,":[140],"obtain":[142],"closed-form":[143],"expressions":[144],"investment":[147],"strategies":[148],"without":[151],"constraint.":[154],"Several":[155],"numerical":[156],"examples":[157],"are":[158],"provided":[159],"illustrate":[161],"impact":[163],"VaR/CVaR/wcCVaR":[167],"other":[170],"parameters":[171],"on":[172],"strategy.":[175]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
