Stochastic optimal control problems under G-expectation
Article first published online: 15 DEC 2011
Copyright © 2011 John Wiley & Sons, Ltd.
Optimal Control Applications and Methods
Volume 34, Issue 1, pages 96–110, January/February 2013
How to Cite
Zhang, D. (2013), Stochastic optimal control problems under G-expectation. Optim. Control Appl. Meth., 34: 96–110. doi: 10.1002/oca.2012
- Issue published online: 15 JAN 2013
- Article first published online: 15 DEC 2011
- Manuscript Accepted: 10 NOV 2011
- Manuscript Revised: 2 DEC 2010
- Manuscript Received: 8 JUL 2010
- stochastic optimal control problems;
- G-Brownian motion
Peng first introduced the notion of G-Brownian motion and G-expectation and established the stochastic calculus with respect to G-Brownian motion in 2006. In this paper, we investigate the stochastic optimal control problems under G-expectation and obtain dynamic programming principle. The value function is proved to be a viscosity solution of a fully nonlinear second-order partial differential equation. A particular case of this equation is the well-known Hamilton–Jacobi–Bellman–Isaacs equation. Copyright © 2011 John Wiley & Sons, Ltd.