{"title":"具有特殊结构的多维二次和次二次BSDEs","authors":"Patrick Cheridito, Kihun Nam","doi":"10.1080/17442508.2015.1013959","DOIUrl":null,"url":null,"abstract":"We study multidimensional BSDEs of the formwith bounded terminal conditions and drivers that grow at most quadratically in . We consider three different cases. In the first case, the BSDE is Markovian, and a solution can be obtained from a solution to a related FBSDE. In the second case, the BSDE becomes a one-dimensional quadratic BSDE when projected to a one-dimensional subspace, and a solution can be derived from a solution of the one-dimensional equation. In the third case, the growth of the driver in is strictly subquadratic, and the existence and uniqueness of a solution can be shown by first solving the BSDE on a short time interval and then extending it recursively.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"53","resultStr":"{\"title\":\"Multidimensional quadratic and subquadratic BSDEs with special structure\",\"authors\":\"Patrick Cheridito, Kihun Nam\",\"doi\":\"10.1080/17442508.2015.1013959\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study multidimensional BSDEs of the formwith bounded terminal conditions and drivers that grow at most quadratically in . We consider three different cases. In the first case, the BSDE is Markovian, and a solution can be obtained from a solution to a related FBSDE. In the second case, the BSDE becomes a one-dimensional quadratic BSDE when projected to a one-dimensional subspace, and a solution can be derived from a solution of the one-dimensional equation. In the third case, the growth of the driver in is strictly subquadratic, and the existence and uniqueness of a solution can be shown by first solving the BSDE on a short time interval and then extending it recursively.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2013-09-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"53\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1080/17442508.2015.1013959\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/17442508.2015.1013959","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Multidimensional quadratic and subquadratic BSDEs with special structure
We study multidimensional BSDEs of the formwith bounded terminal conditions and drivers that grow at most quadratically in . We consider three different cases. In the first case, the BSDE is Markovian, and a solution can be obtained from a solution to a related FBSDE. In the second case, the BSDE becomes a one-dimensional quadratic BSDE when projected to a one-dimensional subspace, and a solution can be derived from a solution of the one-dimensional equation. In the third case, the growth of the driver in is strictly subquadratic, and the existence and uniqueness of a solution can be shown by first solving the BSDE on a short time interval and then extending it recursively.