Premium
A stochastic maximum principle for processes driven by G ‐Brownian motion and applications to finance
Author(s) -
Sun Zhongyang,
Zhang Xin,
Guo Junyi
Publication year - 2017
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2299
Subject(s) - maximum principle , stochastic differential equation , mathematics , continuous time stochastic process , brownian motion , geometric brownian motion , stochastic volatility , convexity , stochastic control , sublinear function , stochastic process , mathematical finance , state space , mathematical economics , mathematical optimization , diffusion process , portfolio , optimal control , volatility (finance) , economics , mathematical analysis , econometrics , finance , statistics , economy , service (business)
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.