Stochastic optimal control problems under G-expectation

Authors

  • Defei Zhang

    Corresponding author
    1. School of Mathematics, Honghe University, Mengzi 661100, China
    • School of Mathematics, Shandong University, Jinan 250100, China
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Defei Zhang, School of Mathematics, Shandong University, Jinan 250100, China.

E-mail: zhdefei@163.com

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.

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