Finite Horizon Stochastic <i>H</i>₂/<i>H</i>_∞ Control for Continuous‐Time Systems Driven by <i>G</i>‐Brownian Motion

ABSTRACT In this article, we consider a stochastic control problem under volatility ambiguity. In this framework, the state function is described by a stochastic differential equation driven by ‐Brownian motion. Different from the classical approach, the volatility ambiguity is characterized by a family of non‐dominated probability measures. control can be modeled as a “inf‐sup problem” and control can be modeled as a “sup‐sup problem.” With the help of stochastic maximum principle and dynamic programming principle, we derive the stochastic bounded real lemma and two sets of cross coupled generalized differential Riccati equations, which is associated with the solvability of control.