{"title":"Optimal controls of backward stochastic differential equations","authors":"Nikolai Dokuchaev, X. Zhou","doi":"10.1109/CDC.1999.830191","DOIUrl":null,"url":null,"abstract":"This paper considers a nonlinear stochastic control problem where the system dynamics is a controlled nonlinear backward stochastic differential equation and the state must coincide with a given random vector at the terminal time. A necessary condition of optimality in the form of a global maximum principle as well as a sufficient condition of optimality are presented. The general result is also applied to a backward linear-quadratic control problem and an optimal control is obtained explicitly as a feedback of the solution to a forward-backward equation. Finally, a nonlinear problem with additional integral constraints is discussed and it is shown that the duality gap is zero under the Slater condition.","PeriodicalId":137513,"journal":{"name":"Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1999-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC.1999.830191","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
This paper considers a nonlinear stochastic control problem where the system dynamics is a controlled nonlinear backward stochastic differential equation and the state must coincide with a given random vector at the terminal time. A necessary condition of optimality in the form of a global maximum principle as well as a sufficient condition of optimality are presented. The general result is also applied to a backward linear-quadratic control problem and an optimal control is obtained explicitly as a feedback of the solution to a forward-backward equation. Finally, a nonlinear problem with additional integral constraints is discussed and it is shown that the duality gap is zero under the Slater condition.