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Stochastic optimal control problems under G‐expectation
Author(s) -
Zhang Defei
Publication year - 2011
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.2012
Subject(s) - bellman equation , brownian motion , viscosity solution , mathematics , stochastic control , stochastic differential equation , geometric brownian motion , dynamic programming , hamilton–jacobi–bellman equation , optimal control , stochastic calculus , partial differential equation , nonlinear system , mathematical economics , mathematical analysis , diffusion process , mathematical optimization , stochastic partial differential equation , computer science , physics , knowledge management , statistics , innovation diffusion , quantum mechanics
SUMMARY 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.