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

arXiv: https://arxiv.org/abs/1309.0209 · HTML: https://mlsanity.com/paper/1309.0209/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Sep 2013.

## Built on by (most cited first, 1 of 1)

- [Research on Optimal Control Problem Based on Reinforcement Learning under Knightian Uncertainty](https://mlsanity.com/paper/2506.13207/) (2025)

## Abstract (arXiv)

By the calculus of Peng's G-sublinear expectation and G-Brownian motion on a sublinear expectation space (Omega, cal H, hatmathbbE), 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.