Equilibrium stochastic control with implicitly defined objective functions

[2312.15173] Equilibrium stochastic control with implicitly defined objective functions Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Optimization and Control arXiv:2312.15173 (math) [Submitted on 23 Dec 2023 ( v1 ), last revised 16 Aug 2026 (this version, v3)] Title: Equilibrium stochastic control with implicitly defined objective functions Authors: Zongxia Liang , Jianming Xia , Keyu Zhang View a PDF of the paper titled Equilibrium stochastic control with implicitly defined objective functions, by Zongxia Liang and 2 other authors View PDF HTML (experimental) Abstract: This paper considers a class of stochastic control problems with implicitly defined objective functions, which are the sources of time-inconsistency. We study the closed-loop equilibrium solutions in a general controlled diffusion framework. First, we provide a sufficient and necessary condition for a strategy to be an equilibrium. Then, we apply the result to discuss two problems of dynamic portfolio selection for a class of betweenness preferences, allowing for closed convex constraints on portfolio weights and borrowing cost, respectively. The equilibrium portfolio strategies are explicitly characterized in terms of the solutions of some first-order ordinary differential equations for the case of deterministic market coefficients. Comments: To appear in SCIENTIA SINICA Mathematica Subjects: Optimization and Control (math.OC) ; Mathematical Finance (q-fin.MF) Cite as: arXiv:2312.15173 [math.OC] (or arXiv:2312.15173v3 [math.OC] for this version) https://doi.org/10.48550/arXiv.2312.15173 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Keyu Zhang [ view email ] [v1] Sat, 23 Dec 2023 06:03:46 UTC (31 KB) [v2] Wed, 27 Dec 2023 02:11:57 UTC (31 KB) [v3] Sun, 16 Aug 2026 10:22:54 UTC (32 KB) Full-text links: Access Paper: View a PDF of the paper titled Equilibrium stochastic control with implicitly defined objective functions, by Zongxia Liang and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2023-12 Change to browse by: math q-fin q-fin.MF References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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