A local maximum principle for robust optimal control problems of quadratic BSDEs

TL;DR

This paper establishes a necessary maximum principle for robust optimal control of quadratic BSDEs with uncertain models, involving advanced techniques to handle unbounded coefficients and parameter sensitivity.

Contribution

It introduces a new maximum principle for quadratic BSDE control problems with model uncertainty, utilizing weak convergence and inequalities to handle unbounded coefficients.

Findings

Proved the variational inequality using weak convergence.

Established continuity of solutions with respect to parameter .

Derived necessary and sufficient conditions for robust optimal control.

Abstract

The paper concerns the necessary maximum principle for robust optimal control problems of quadratic BSDEs. The coefficient of the systems depends on the parameter $\theta$, and the generator of BSDEs is of quadratic growth in $z$. Since the model is uncertain, the variational inequality is proved by weak convergence technique. In addition, due to the generator being quadratic with respect to $z$, the forward adjoint equations are SDEs with unbounded coefficient involving mean oscillation martingales. Using reverse H\"older inequality and John-Nirenberg inequality, we show that its solutions are continuous with respect to the parameter $\theta$. The necessary and sufficient conditions for robust optimal control are proved by linearization method.