{"title":"Robust Time-Inconsistent Linear-Quadratic Stochastic Controls: A Stochastic Differential Game Approach","authors":"Bingyan Han, Chi Seng Pun, Hoi Ying Wong","doi":"10.1007/s00245-025-10310-1","DOIUrl":null,"url":null,"abstract":"<div><p>This paper studies robust time-inconsistent (TIC) linear-quadratic stochastic control problems, formulated by stochastic differential games. By a spike variation approach, we derive sufficient conditions for achieving the Nash equilibrium, which corresponds to a time-consistent (TC) robust policy, under mild technical assumptions. To illustrate our framework, we consider two scenarios of robust mean-variance analysis, namely with state- and control-dependent ambiguity aversion. We find numerically that with time inconsistency haunting the dynamic optimal controls, the ambiguity aversion enhances the effective risk aversion faster than the linear, implying that the ambiguity in the TIC cases is more impactful than that under the TC counterparts, e.g., expected utility maximization problems.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"92 2","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2025-09-15","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/s00245-025-10310-1","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 studies robust time-inconsistent (TIC) linear-quadratic stochastic control problems, formulated by stochastic differential games. By a spike variation approach, we derive sufficient conditions for achieving the Nash equilibrium, which corresponds to a time-consistent (TC) robust policy, under mild technical assumptions. To illustrate our framework, we consider two scenarios of robust mean-variance analysis, namely with state- and control-dependent ambiguity aversion. We find numerically that with time inconsistency haunting the dynamic optimal controls, the ambiguity aversion enhances the effective risk aversion faster than the linear, implying that the ambiguity in the TIC cases is more impactful than that under the TC counterparts, e.g., expected utility maximization problems.
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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