1. Social Optima in Mean Field Linear-Quadratic-Gaussian Control with Volatility Uncertainty
- Author
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Jiongmin Yong, Bing-Chang Wang, and Jianhui Huang
- Subjects
0209 industrial biotechnology ,Control and Optimization ,Applied Mathematics ,010102 general mathematics ,02 engineering and technology ,Mean field game ,Linear-quadratic-Gaussian control ,01 natural sciences ,020901 industrial engineering & automation ,Mean field theory ,Optimization and Control (math.OC) ,FOS: Mathematics ,Applied mathematics ,0101 mathematics ,Common noise ,Diffusion (business) ,Volatility (finance) ,Mathematics - Optimization and Control ,Social optimum ,Mathematics - Abstract
This paper examines mean field linear-quadratic-Gaussian (LQG) 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.
- Published
- 2021