{"title":"具有确定性系数的BSDE的唯一性结果","authors":"Yufeng Shi, Zhi Yang","doi":"10.3934/puqr.2023013","DOIUrl":null,"url":null,"abstract":"In this paper, we study one-dimensional backward stochastic differential equation (BSDE), whose deterministic coefficient $f$ is Lipschitz in $y$ but only continuous in $z$. If the terminal condition $\\xi$ has bounded Malliavin derivative, we prove some uniqueness results for the BSDE with quadratic and linear growth in $z$, respectively.","PeriodicalId":42330,"journal":{"name":"Probability Uncertainty and Quantitative Risk","volume":"18 1","pages":"0"},"PeriodicalIF":1.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the uniqueness result for the BSDE with deterministic coefficient\",\"authors\":\"Yufeng Shi, Zhi Yang\",\"doi\":\"10.3934/puqr.2023013\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we study one-dimensional backward stochastic differential equation (BSDE), whose deterministic coefficient $f$ is Lipschitz in $y$ but only continuous in $z$. If the terminal condition $\\\\xi$ has bounded Malliavin derivative, we prove some uniqueness results for the BSDE with quadratic and linear growth in $z$, respectively.\",\"PeriodicalId\":42330,\"journal\":{\"name\":\"Probability Uncertainty and Quantitative Risk\",\"volume\":\"18 1\",\"pages\":\"0\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Probability Uncertainty and Quantitative Risk\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3934/puqr.2023013\",\"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":"1085","ListUrlMain":"https://doi.org/10.3934/puqr.2023013","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
On the uniqueness result for the BSDE with deterministic coefficient
In this paper, we study one-dimensional backward stochastic differential equation (BSDE), whose deterministic coefficient $f$ is Lipschitz in $y$ but only continuous in $z$. If the terminal condition $\xi$ has bounded Malliavin derivative, we prove some uniqueness results for the BSDE with quadratic and linear growth in $z$, respectively.
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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