A stochastic maximum principle for processes driven by G-Brownian motion and applications to finance

摘要

On the basis of the theory of stochastic differential equations on a sublinear expectation space (H,E), we develop a stochastic maximum principle for a general stochastic optimal control problem, where the controlled state process is a stochastic differential equation driven by G-Brownian motion. Furthermore, under some convexity assumptions, we obtain sufficient conditions for the optimality of the maximum in terms of the H-function. Finally, applications of the stochastic maximum principle to the mean-variance portfolio selection problem in the financial market with ambiguous volatility is discussed.