Social optima in mean field linear-quadratic-Gaussian control with volatility uncertainty

Jianhui Huang, Bing Chang Wang, Jiongmin Yong

Research output: Journal article publicationJournal articleAcademic researchpeer-review

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.

Original languageEnglish
Pages (from-to)825-856
Number of pages32
JournalSIAM Journal on Control and Optimization
Volume59
Issue number2
DOIs
Publication statusE-pub ahead of print - 1 Mar 2021

Keywords

  • Common noise
  • Forward-backward stochastic differential equation
  • Mean field game
  • Social control
  • Uncertainty

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

Cite this