{"title":"一般约束下具有Epstein-Zin效用的最优消费与投资组合选择","authors":"Zixin Feng, D. Tian","doi":"10.3934/puqr.2023012","DOIUrl":null,"url":null,"abstract":"The paper investigates the consumption-investment problem for an investor with Epstein-Zin utility in an incomplete market. Closed, not necessarily convex, constraints are imposed on strategies. The optimal consumption and investment strategies are characterized via a quadratic backward stochastic differential equation (BSDE). Due to the stochastic market environment, the solution to this BSDE is unbounded and thereby the BMO argument breaks down. After establishing the martingale optimality criterion, by delicately selecting Lyapunov functions, the verification theorem is ultimately obtained. Besides, several examples and numerical simulations for the optimal strategies are provided and illustrated.","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"29 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2021-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Optimal consumption and portfolio selection with Epstein–Zin utility under general constraints\",\"authors\":\"Zixin Feng, D. Tian\",\"doi\":\"10.3934/puqr.2023012\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The paper investigates the consumption-investment problem for an investor with Epstein-Zin utility in an incomplete market. Closed, not necessarily convex, constraints are imposed on strategies. The optimal consumption and investment strategies are characterized via a quadratic backward stochastic differential equation (BSDE). Due to the stochastic market environment, the solution to this BSDE is unbounded and thereby the BMO argument breaks down. After establishing the martingale optimality criterion, by delicately selecting Lyapunov functions, the verification theorem is ultimately obtained. Besides, several examples and numerical simulations for the optimal strategies are provided and illustrated.\",\"PeriodicalId\":42330,\"journal\":{\"name\":\"Probability Uncertainty and Quantitative Risk\",\"volume\":\"29 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2021-11-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Probability Uncertainty and Quantitative Risk\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3934/puqr.2023012\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Probability Uncertainty and Quantitative Risk","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/puqr.2023012","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Optimal consumption and portfolio selection with Epstein–Zin utility under general constraints
The paper investigates the consumption-investment problem for an investor with Epstein-Zin utility in an incomplete market. Closed, not necessarily convex, constraints are imposed on strategies. The optimal consumption and investment strategies are characterized via a quadratic backward stochastic differential equation (BSDE). Due to the stochastic market environment, the solution to this BSDE is unbounded and thereby the BMO argument breaks down. After establishing the martingale optimality criterion, by delicately selecting Lyapunov functions, the verification theorem is ultimately obtained. Besides, several examples and numerical simulations for the optimal strategies are provided and illustrated.
期刊介绍：
Probability, Uncertainty and Quantitative Risk (PUQR) is a quarterly academic journal under the supervision of the Ministry of Education of the People's Republic of China and hosted by Shandong University, which is open to the public at home and abroad (ISSN 2095-9672; CN 37-1505/O1).
Probability, Uncertainty and Quantitative Risk (PUQR) mainly reports on the major developments in modern probability theory, covering stochastic analysis and statistics, stochastic processes, dynamical analysis and control theory, and their applications in the fields of finance, economics, biology, and computer science. The journal is currently indexed in ESCI, Scopus, Mathematical Reviews, zbMATH Open and other databases.
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