@article{8b238176ee3f48baa33ebb5c44eb3c3d,
title = "Social optima in mean field linear-quadratic-Gaussian control with volatility uncertainty",
abstract = "This paper examines mean field linear-quadratic-Gaussian social optimum control with volatility-uncertain common noise. The diffusion terms in the dynamics of agents contain an unknown volatility process driven by a common noise. We apply a robust optimization approach in which all agents view volatility uncertainty as an adversarial player. Based on the principle of person-by-person optimality and a two-step duality technique for stochastic variational analysis, we construct an auxiliary optimal control problem for a representative agent. Through solving this problem combined with a consistent mean field approximation, we design a set of decentralized strategies, which are further shown to be asymptotically social optimal by perturbation analysis.",
keywords = "Common noise, Forward-backward stochastic differential equation, Mean field game, Social control, Uncertainty",
author = "Jianhui Huang and Wang, {Bing Chang} and Jiongmin Yong",
note = "Funding Information: \ast Received by the editors December 13, 2019; accepted for publication (in revised form) November 24, 2020; published electronically March 1, 2021. https://doi.org/10.1137/19M1306737 Funding: This work was funded in part by RGC Early Career Scheme (ECS) grants 502412P and 500613P, by the National Natural Science Foundation of China under grant 61773241, by NSF grant DMS-1812921, and in part by the PolyU-SDU Joint Research Centre on Financial Mathematics. \dagger Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong (
[email protected]). \ddagger School of Control Science and Engineering, Shandong University, Jinan 250061, People's Republic of China (
[email protected]). \S Department of Mathematics, University of Central Florida, Orlando, FL 32816 USA (jiongmin.
[email protected]). Publisher Copyright: {\textcopyright} 2021 Society for Industrial and Applied Mathematics",
year = "2021",
month = mar,
day = "1",
doi = "10.1137/19M1306737",
language = "English",
volume = "59",
pages = "825--856",
journal = "SIAM Journal on Control and Optimization",
issn = "0363-0129",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "2",
}