A stochastic maximum principle for processes driven by G‐Brownian motion and applications to finance. (31st January 2017)

• Record Type: Journal Article
• Authors: Sun, Zhongyang; Zhang, Xin; Guo, Junyi
• Is Part Of: Optimal control applications and methods. Volume 38:Number 6(2017)
• Page Start: 934
• Page End: 948
• Publication Date: 2017-01-31
• Subjects: ambiguous volatility -- G‐Brownian motion -- G‐expectation -- model uncertainty -- stochastic maximum principle -- stochastic optimal control; Control theory -- Periodicals; Mathematical optimization -- Periodicals; 629.8312
• DOI: 10.1002/oca.2299
• Languages: English
• ISSNs: 0143-2087

Abstract

Summary: On the basis of the theory of stochastic differential equations on a sublinear expectation space ( Ω, 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.