Please use this identifier to cite or link to this item:
http://hdl.handle.net/10397/93871
Title: | Social optima in mean field linear-quadratic-Gaussian control with volatility uncertainty | Authors: | Huang, J Wang, BC Yong, J |
Issue Date: | 2021 | Source: | SIAM journal on control and optimization, 2021, v. 59, no. 2, p. 825-856 | 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 |
Publisher: | Society for Industrial and Applied Mathematics | Journal: | SIAM journal on control and optimization | ISSN: | 0363-0129 | EISSN: | 1095-7138 | DOI: | 10.1137/19M1306737 | Rights: | © 2021 Society for Industrial and Applied Mathematics The following publication Huang, J., Wang, B. C., & Yong, J. (2021). Social optima in mean field linear-quadratic-Gaussian control with volatility uncertainty. SIAM Journal on Control and Optimization, 59(2), 825-856 is available at https://doi.org/10.1137/19M1306737 |
Appears in Collections: | Journal/Magazine Article |
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