Optimal stochastic control and optimal consumption and portfolio with G-Brownian motion

Weiyin Fei, Chen Fei

Published 2013-09-01Version 1

By the calculus of Peng's G-sublinear expectation and G-Brownian motion on a sublinear expectation space $(\Omega, {\cal H}, \hat{\mathbb{E}})$, we first set up an optimality principle of stochastic control problem. Then we investigate an optimal consumption and portfolio decision with a volatility ambiguity by the derived verification theorem. Next the two-fund separation theorem is explicitly obtained. And an illustrative example is provided.