{"id":"https://openalex.org/W3133637382","doi":"https://doi.org/10.68381/jca29035","title":"New Jensen-Type Inequalities and their Applications","display_name":"New Jensen-Type Inequalities and their Applications","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W3133637382","doi":"https://doi.org/10.68381/jca29035","mag":"3133637382"},"language":"en","primary_location":{"id":"doi:10.68381/jca29035","doi":"https://doi.org/10.68381/jca29035","is_oa":true,"landing_page_url":"https://doi.org/10.68381/jca29035","pdf_url":"https://journalofconvexanalysis.com/articles/jca29035/jca29035.pdf","source":{"id":"https://openalex.org/S163398844","display_name":"Journal of convex analysis","issn_l":"0944-6532","issn":["0944-6532","2363-6394"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-2"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Convex Analysis","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://journalofconvexanalysis.com/articles/jca29035/jca29035.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081397806","display_name":"Bar Light","orcid":"https://orcid.org/0000-0002-6123-7568","observed_orcids":["https://orcid.org/0000-0002-6123-7568"]},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Bar Light","raw_affiliation_strings":["Graduate School of Business, Stanford University, Stanford, U.S.A","Stanford University ()"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of Business, Stanford University, Stanford, U.S.A","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Stanford University ()","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5081397806"],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.00758112,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":93},"biblio":{"volume":"29","issue":"2","first_page":"605","last_page":"622"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/jensen-type-inequalities","display_name":"Jensen-type inequalities","score":0.9909999966621399},{"id":"https://openalex.org/keywords/risk-aversion","display_name":"risk aversion","score":0.9139999747276306},{"id":"https://openalex.org/keywords/risk-measures","display_name":"risk measures","score":0.890999972820282},{"id":"https://openalex.org/keywords/poisson-approximation","display_name":"Poisson approximation","score":0.9319999814033508},{"id":"https://openalex.org/keywords/moment-generating-function","display_name":"moment generating function","score":1.0},{"id":"https://openalex.org/keywords/log-likelihood","display_name":"log-likelihood","score":0.9990000128746033},{"id":"https://openalex.org/keywords/hermite-hadamard-inequality","display_name":"Hermite-Hadamard inequality","score":0.8799999952316284},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"convex analysis","score":0.6290000081062317}],"concepts":[{"id":"https://openalex.org/C174169938","wikidata":"https://www.wikidata.org/wiki/Q518131","display_name":"Jensen's inequality","level":5,"score":0.7215687036514282},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6917707324028015},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.6715904474258423},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.6450716257095337},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6206672191619873},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.512423574924469},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.5082663893699646},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.49645835161209106},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.49552977085113525},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.47350719571113586},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4718577563762665},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.4669780433177948},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43095892667770386},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4111926257610321},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3846929371356964},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.3607766628265381},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.29982584714889526},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20158827304840088},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10096561908721924},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.68381/jca29035","doi":"https://doi.org/10.68381/jca29035","is_oa":true,"landing_page_url":"https://doi.org/10.68381/jca29035","pdf_url":"https://journalofconvexanalysis.com/articles/jca29035/jca29035.pdf","source":{"id":"https://openalex.org/S163398844","display_name":"Journal of convex analysis","issn_l":"0944-6532","issn":["0944-6532","2363-6394"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-2"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Convex Analysis","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:arx:papers:2007.09258","doi":null,"is_oa":false,"landing_page_url":"http://arxiv.org/pdf/2007.09258","pdf_url":"http://arxiv.org/pdf/2007.09258","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,"listed_in":[],"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"},{"id":"pmh:oai:arXiv.org:2007.09258","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2007.09258","pdf_url":"https://arxiv.org/pdf/2007.09258","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"mag:3133637382","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2007.09258.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2007.09258","doi":"https://doi.org/10.48550/arxiv.2007.09258","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2007.09258","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.68381/jca29035","doi":"https://doi.org/10.68381/jca29035","is_oa":true,"landing_page_url":"https://doi.org/10.68381/jca29035","pdf_url":"https://journalofconvexanalysis.com/articles/jca29035/jca29035.pdf","source":{"id":"https://openalex.org/S163398844","display_name":"Journal of convex analysis","issn_l":"0944-6532","issn":["0944-6532","2363-6394"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-2"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Convex Analysis","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3133637382.pdf","grobid_xml":"https://content.openalex.org/works/W3133637382.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W47555992","https://openalex.org/W1524687023","https://openalex.org/W1983466306","https://openalex.org/W2006458314","https://openalex.org/W2019291268","https://openalex.org/W2049633694","https://openalex.org/W2056135743","https://openalex.org/W2058860749","https://openalex.org/W2075696195","https://openalex.org/W2168167223","https://openalex.org/W2519050643","https://openalex.org/W2580645530","https://openalex.org/W2887948261","https://openalex.org/W2966963070","https://openalex.org/W3087747475","https://openalex.org/W3123938297","https://openalex.org/W3124281196","https://openalex.org/W3125997868","https://openalex.org/W3151142870"],"related_works":["https://openalex.org/W3043469727","https://openalex.org/W2135210132","https://openalex.org/W2029039201","https://openalex.org/W2091751674","https://openalex.org/W2125097487","https://openalex.org/W2381656362","https://openalex.org/W2094883014","https://openalex.org/W2197650538","https://openalex.org/W2517438223","https://openalex.org/W91964248"],"abstract_inverted_index":{"Convex":[0],"analysis":[1],"is":[2],"fundamental":[3],"to":[4,36,42,49,57],"proving":[5],"inequalities":[6,24,33,56],"that":[7,27],"have":[8],"a":[9],"wide":[10],"variety":[11],"of":[12],"applications":[13,99],"in":[14,71,75,80,97],"economics":[15],"and":[16,38,44,74,84,113],"mathematics.":[17],"In":[18],"this":[19],"paper":[20],"we":[21],"provide":[22],"Jensen-type":[23],"for":[25],"functions":[26],"are,":[28],"intuitively,":[29],"\"very\"":[30],"convex.":[31],"These":[32],"are":[34],"simple":[35],"apply":[37,54,94],"can":[39],"be":[40],"used":[41],"generalize":[43],"extend":[45],"previous":[46],"results":[47,96],"or":[48],"derive":[50],"new":[51],"results.":[52],"We":[53,92],"our":[55,95],"quantify":[58],"the":[59,72,76],"notion":[60],"\"more":[61],"risk":[62,104],"averse\"":[63],"provided":[64],"by":[65],"J.":[66],"W.":[67],"Pratt":[68],"[Risk":[69],"aversion":[70],"small":[73],"large,":[77],"in:":[78],"Uncertainty":[79],"Economics,":[81],"P.":[82],"Diamond":[83],"M.":[85],"Rothschild":[86],"(eds.),":[87],"Elsevier,":[88],"Amsterdam":[89],"(1978)":[90],"59\u201379].":[91],"also":[93],"other":[98],"from":[100],"different":[101],"fields,":[102],"including":[103],"measures,":[105],"Poisson":[106],"approximation,":[107],"moment":[108],"generating":[109],"functions,":[110,112],"log-likelihood":[111],"Hermite-Hadamard":[114],"type":[115],"inequalities.":[116]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2021-03-15T00:00:00"}
