{"title":"随机最优控制","authors":"T. Björk","doi":"10.1093/oso/9780198851615.003.0025","DOIUrl":null,"url":null,"abstract":"We study a general stochastic optimal control problem within the framework of a controlled SDE. This problem is studied using dynamic programming and we derive the Hamilton–Jacobi–Bellman PDE. By stating and proving a verification theorem we show that solving this PDE is equivalent to solving the control problem. As an example the theory is then applied to the linear quadratic regulator.","PeriodicalId":311283,"journal":{"name":"Arbitrage Theory in Continuous Time","volume":"24 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1998-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stochastic Optimal Control\",\"authors\":\"T. Björk\",\"doi\":\"10.1093/oso/9780198851615.003.0025\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study a general stochastic optimal control problem within the framework of a controlled SDE. This problem is studied using dynamic programming and we derive the Hamilton–Jacobi–Bellman PDE. By stating and proving a verification theorem we show that solving this PDE is equivalent to solving the control problem. As an example the theory is then applied to the linear quadratic regulator.\",\"PeriodicalId\":311283,\"journal\":{\"name\":\"Arbitrage Theory in Continuous Time\",\"volume\":\"24 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1998-09-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Arbitrage Theory in Continuous Time\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1093/oso/9780198851615.003.0025\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Arbitrage Theory in Continuous Time","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/oso/9780198851615.003.0025","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We study a general stochastic optimal control problem within the framework of a controlled SDE. This problem is studied using dynamic programming and we derive the Hamilton–Jacobi–Bellman PDE. By stating and proving a verification theorem we show that solving this PDE is equivalent to solving the control problem. As an example the theory is then applied to the linear quadratic regulator.
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