{"title":"Well-Posedness of Infinite Horizon FBSDEs with Non-zero Terminals and LQ Problems with Random Coefficients","authors":"Jinghua Li, Zhiyong Yu","doi":"10.1007/s00245-025-10263-5","DOIUrl":null,"url":null,"abstract":"<div><p>This paper is concerned with fully coupled forward–backward stochastic differential equations (FBSDEs, for short) with non-zero terminals in infinite horizon. By introducing stochastic Lipschitz conditions and constructing infinite horizon domination–monotonicity conditions, the well-posedness of this kind of infinite horizon FBSDEs including the existence, uniqueness and a pair of estimates is proved. Moreover, the theoretical results are applied to solve four kinds of linear-quadratic (LQ, for short) stochastic optimal control problems with random coefficients in infinite horizon. Due to the unboundedness and randomness of coefficients, the results of the FBSDEs and LQ problems obtained in this paper, even if they are degenerated to finite horizon, contain more situations than the results in the literature.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 3","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2025-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Optimization","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00245-025-10263-5","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
This paper is concerned with fully coupled forward–backward stochastic differential equations (FBSDEs, for short) with non-zero terminals in infinite horizon. By introducing stochastic Lipschitz conditions and constructing infinite horizon domination–monotonicity conditions, the well-posedness of this kind of infinite horizon FBSDEs including the existence, uniqueness and a pair of estimates is proved. Moreover, the theoretical results are applied to solve four kinds of linear-quadratic (LQ, for short) stochastic optimal control problems with random coefficients in infinite horizon. Due to the unboundedness and randomness of coefficients, the results of the FBSDEs and LQ problems obtained in this paper, even if they are degenerated to finite horizon, contain more situations than the results in the literature.
期刊介绍：
The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.
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