{"title":"反映后向随机微分方程的动态规划方法","authors":"Hun O, Mun-Chol Kim, Kon-Gun Kim","doi":"10.1214/23-ejp999","DOIUrl":null,"url":null,"abstract":"By introducing a new type of minimality condition, this paper gives a novel approach to the reflected backward stochastic differential equations (RBSDEs) with càdlàg obstacles. Our first step is to prove the dynamic programming principles for nonlinear optimal stopping problems with g-expectations. We then use the nonlinear Doob-Meyer decomposition theorem for g-supermartingales to get the existence of the solution. With a new type of minimality condition, we prove a representation formula of solutions to RBSDEs, in an efficient way. Finally, we derive some a priori estimates and stability results.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":"36 1","pages":"0"},"PeriodicalIF":1.3000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Dynamic programming approach to reflected backward stochastic differential equations\",\"authors\":\"Hun O, Mun-Chol Kim, Kon-Gun Kim\",\"doi\":\"10.1214/23-ejp999\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"By introducing a new type of minimality condition, this paper gives a novel approach to the reflected backward stochastic differential equations (RBSDEs) with càdlàg obstacles. Our first step is to prove the dynamic programming principles for nonlinear optimal stopping problems with g-expectations. We then use the nonlinear Doob-Meyer decomposition theorem for g-supermartingales to get the existence of the solution. With a new type of minimality condition, we prove a representation formula of solutions to RBSDEs, in an efficient way. Finally, we derive some a priori estimates and stability results.\",\"PeriodicalId\":50538,\"journal\":{\"name\":\"Electronic Journal of Probability\",\"volume\":\"36 1\",\"pages\":\"0\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Journal of Probability\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1214/23-ejp999\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Journal of Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1214/23-ejp999","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Dynamic programming approach to reflected backward stochastic differential equations
By introducing a new type of minimality condition, this paper gives a novel approach to the reflected backward stochastic differential equations (RBSDEs) with càdlàg obstacles. Our first step is to prove the dynamic programming principles for nonlinear optimal stopping problems with g-expectations. We then use the nonlinear Doob-Meyer decomposition theorem for g-supermartingales to get the existence of the solution. With a new type of minimality condition, we prove a representation formula of solutions to RBSDEs, in an efficient way. Finally, we derive some a priori estimates and stability results.
期刊介绍:
The Electronic Journal of Probability publishes full-size research articles in probability theory. The Electronic Communications in Probability (ECP), a sister journal of EJP, publishes short notes and research announcements in probability theory.
Both ECP and EJP are official journals of the Institute of Mathematical Statistics
and the Bernoulli society.