Social Optima in Mean Field Linear-Quadratic-Gaussian Control with Volatility Uncertainty
| Autor: | Jiongmin Yong, Bing-Chang Wang, Jianhui Huang |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
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 |
| Zdroj: | SIAM Journal on Control and Optimization. 59:825-856 |
| ISSN: | 1095-7138 0363-0129 |
| DOI: | 10.1137/19m1306737 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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