{"title":"律不变凹效用函数与单调与共单调约束的优化问题","authors":"G. Carlier, R. Dana","doi":"10.1524/STND.2006.24.1.127","DOIUrl":null,"url":null,"abstract":"SUMMARY This paper considers a class of one dimensional calculus of variations problems with monotonicity and comonotonicity constraints arising in economic and financial models where law invariant concave criteria (or law invariant convex measures of risk) are used. Existence solutions, optimality conditions, sufficient conditions for the regularity of solutions are established. Applications to risk sharing with convex comonotone law invariant risk measures or with robust utilities are given.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2006-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1524/STND.2006.24.1.127","citationCount":"42","resultStr":"{\"title\":\"Law invariant concave utility functions and optimization problems with monotonicity and comonotonicity constraints\",\"authors\":\"G. Carlier, R. Dana\",\"doi\":\"10.1524/STND.2006.24.1.127\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SUMMARY This paper considers a class of one dimensional calculus of variations problems with monotonicity and comonotonicity constraints arising in economic and financial models where law invariant concave criteria (or law invariant convex measures of risk) are used. Existence solutions, optimality conditions, sufficient conditions for the regularity of solutions are established. Applications to risk sharing with convex comonotone law invariant risk measures or with robust utilities are given.\",\"PeriodicalId\":44159,\"journal\":{\"name\":\"Statistics & Risk Modeling\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2006-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1524/STND.2006.24.1.127\",\"citationCount\":\"42\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Statistics & Risk Modeling\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1524/STND.2006.24.1.127\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistics & Risk Modeling","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1524/STND.2006.24.1.127","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Law invariant concave utility functions and optimization problems with monotonicity and comonotonicity constraints
SUMMARY This paper considers a class of one dimensional calculus of variations problems with monotonicity and comonotonicity constraints arising in economic and financial models where law invariant concave criteria (or law invariant convex measures of risk) are used. Existence solutions, optimality conditions, sufficient conditions for the regularity of solutions are established. Applications to risk sharing with convex comonotone law invariant risk measures or with robust utilities are given.
期刊介绍：
Statistics & Risk Modeling (STRM) aims at covering modern methods of statistics and probabilistic modeling, and their applications to risk management in finance, insurance and related areas. The journal also welcomes articles related to nonparametric statistical methods and stochastic processes. Papers on innovative applications of statistical modeling and inference in risk management are also encouraged. Topics Statistical analysis for models in finance and insurance Credit-, market- and operational risk models Models for systemic risk Risk management Nonparametric statistical inference Statistical analysis of stochastic processes Stochastics in finance and insurance Decision making under uncertainty.
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