Stochastic Linear-Quadratic Mean-Field Games of Controls for Delayed Systems with Jump Diffusion

Na Li (), Yilin Wei () and Qingfeng Zhu ()
Additional contact information
Na Li: Shandong University of Finance and Economics
Yilin Wei: Shandong University of Finance and Economics
Qingfeng Zhu: Shandong University of Finance and Economics

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 3, No 10, 34 pages

Abstract: Abstract In this paper, we investigate a class of stochastic linear-quadratic (LQ) mean-field games (MFGs) for large-population (LP) systems, where the dynamic of each agent is described by a stochastic differential delayed equation with Brownian motions and Poisson jumps. Based on the MFG theory, agents are influenced by both individual and common information when formulating strategies in the stochastic LP system. Firstly, we solve the LQ-MFG of control problem for the stochastic LP system with delay and Poisson jumps by employing the stochastic Hamiltonian system. Secondly, using a separation technique, we derive an asymptotic representation of the average control term. Thirdly, we obtain an explicit representation of the decentralized optimal control for each agent in open-loop form, and in closed-loop form for a special case. Then, we rigorously prove that the set of these decentralized optimal controls constitutes an $$\epsilon $$ ϵ -Nash equilibrium. Finally, to illustrate the theoretical findings, we apply our framework to a monetary asset management problem and validate the results through numerical simulations.

Keywords: Large-population; Mean-field games of controls; Anticipated forward-backward stochastic differential delayed equation; Poisson jumps; $$\epsilon $$ ϵ -Nash equilibrium (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-025-02730-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:206:y:2025:i:3:d:10.1007_s10957-025-02730-4

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-025-02730-4

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().